22:
1504:, but the first definitions are more amenable for constructing lower-brow examples for certain kinds of schemes, such as ones with components of varying dimension. In this way, the structure of the virtual fundamental classes becomes more transparent, giving more intuition for their behavior and structure.
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The first map in the definition of the Gysin morphism corresponds to specializing to the normal cone, which is essentially the first part of the standard Gysin morphism, as defined in Fulton. But, because we are not working with smooth varieties, Fulton's cone construction doesn't work, since it
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We can understand the motivation for the definition of the virtual fundamental class by considering what situation should be emulated for a simple case (such as a smooth complete intersection). Suppose we have a variety
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which has better behavior with respect to the enumerative problems being considered. In this way, there exists a cycle with can be used for answering specific enumerative problems, such as the number of degree
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for which there is an embedding, we must rely upon deformation theory techniques to construct this cycle on the moduli space representing the fundamental class. Now in the case where we have the section
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whose components consist of one degree 3 curve which contracts to a point. There is a virtual fundamental class which can then be used to count the number of curves in this family.
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417:, their behavior can be wild at the boundary, such as having higher-dimensional components at the boundary than on the main space. One such example is in the moduli space
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act as the tangent and obstruction sheaves. Note the construction of
Behrend-Fantechi is a dualization of the exact sequence given from the concrete example above.
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2998:. John, March 21- Morgan, Dusa McDuff, Mohammad Tehrani, Kenji Fukaya, Dominic D. Joyce, Simons Center for Geometry and Physics. Providence, Rhode Island. 2019.
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2138:{\displaystyle A_{*}(Y)\xrightarrow {\sigma } A_{*}(C_{X/Y})\xrightarrow {i_{*}} A_{*}(E_{X/Y})\xrightarrow {0_{E_{X/Y}}^{!}} A_{*-r}(X)}
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One of the first definitions of a virtual fundamental class is for the following case: suppose we have an embedding of a scheme
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There are multiple definitions of virtual fundamental classes, all of which are subsumed by the definition for morphisms of
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Thomas, R. P. (2001-06-11). "A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations".
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Siebert, Bernd (2005-09-04). "Virtual fundamental classes, global normal cones and Fulton's canonical classes".
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Li, Jun; Tian, Gang (1998-02-13). "Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties".
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where the last term represents the "obstruction sheaf". For the general case there is an exact sequence
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Now, this situation dealt with in Fulton-MacPherson intersection theory by looking at the induced cone
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1329:{\displaystyle 0\to {\mathcal {T}}_{1}\to E_{1}\to E_{2}\to {\mathcal {T}}_{2}\to 0}
1237:{\displaystyle 0\to T_{X}\to T_{Y}|_{X}\xrightarrow {ds} E|_{X}\to {\text{ob}}\to 0}
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Kontsevich, M. (1995-06-27). "Enumeration of rational curves via torus actions".
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in the map since it corresponds to the zero section of vector bundle. Then, the
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Virtual fundamental classes, global normal cones and Fulton's canonical classes
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Pandharipande, R.; Thomas, R. P. (2014). "13/2 ways of counting curves". In
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1834:{\displaystyle E_{X/Y}=\bigoplus _{j=1}^{r}i^{*}{\mathcal {O}}_{Y}(-D_{j})}
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where it is transverse, then we can get a homology cycle by looking at the
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Pandharipande, R.; Thomas, R. P. (2014). "13/2 ways of counting curves".
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which is just the generalized Gysin morphism of the fundamental class of
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2857:. Kentaro Hori. Providence, RI: American Mathematical Society. 2003.
2718:; Newstead, Peter; Thomas, Richard P. W; Garcia-Prada, Oscar (eds.).
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488:{\displaystyle {\overline {\mathcal {M}}}_{1,n}(\mathbb {P} ^{2},1)}
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1736:. One natural candidate for such an obstruction bundle if given by
2778:(2020-04-09). "Virtual classes for the working mathematician".
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Symmetry, Integrability and
Geometry: Methods and Applications
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Virtual fundamental class of an embedding into a smooth scheme
15:
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using the generalized Gysin morphism given by the composition
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for the divisors associated to a non-zero set of generators
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on the induced cone and the zero section, giving a cycle on
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2551:{\displaystyle _{E_{X/Y}}^{\text{vir}}:=f_{E_{X/Y}}^{!}()}
1929:. Then, we can construct the virtual fundamental class of
331:{\displaystyle {\overline {\mathcal {M}}}_{g,n}(X,\beta )}
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and looking at the intersection of the induced section
623:(representing the coarse space of some moduli problem
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2419:{\displaystyle \pi ^{*}:A_{k-r}(X)\to A_{k}(E_{X/Y})}
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1477:{\displaystyle {\mathcal {T}}_{1},{\mathcal {T}}_{2}}
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is a replacement of the classical fundamental class
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2995:Virtual fundamental cycles in symplectic topology
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167:{\displaystyle _{E^{\bullet }}^{\text{vir}}}
3075:(N ed.). New York: Springer New York.
953:. This bundle acts as the normal bundle of
3026:: CS1 maint: location missing publisher (
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106:Learn how and when to remove this message
865:is not, and it lies within a sub-bundle
2774:Battistella, Luca; Carocci, Francesca;
2706:
1488:Remark on definitions and special cases
1068:. If there is no obvious ambient space
584:{\displaystyle f:C\to \mathbb {P} ^{2}}
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1141:, there is a four term exact sequence
7:
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2639:{\displaystyle C_{X/Y}\cong N_{X/Y}}
1922:{\displaystyle {\mathcal {I}}_{X/Y}}
1579:{\displaystyle i:X\hookrightarrow Y}
44:adding citations to reliable sources
2454:of the previous setup is defined as
1883:{\displaystyle f_{1},\ldots ,f_{r}}
14:
1636:{\displaystyle \pi :E_{X/Y}\to X}
1429:{\displaystyle T_{Y}|_{X},E|_{X}}
1589:and a vector bundle (called the
845:is a transverse section, but if
540:{\displaystyle \mathbb {P} ^{2}}
20:
2324:{\displaystyle 0_{E_{X/Y}}^{!}}
2188:{\displaystyle f_{E_{X/Y}}^{!}}
31:needs additional citations for
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640:{\displaystyle {\mathcal {X}}}
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2738:10.1017/CBO9781107279544.007
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235:{\displaystyle \in A^{*}(X)}
2585:Remarks on the construction
1372:{\displaystyle E_{1},E_{2}}
889:{\displaystyle E'\subset E}
55:"Virtual fundamental class"
3133:
2274:{\displaystyle \sigma ()=}
1646:such that the normal cone
1502:perfect obstruction theory
2452:virtual fundamental class
128:virtual fundamental class
3069:Fulton, William (1998).
2666:relevant to the variety
1114:{\displaystyle s:Y\to E}
753:has "virtual dimension"
410:{\displaystyle A_{1}(X)}
277:Kontsevich moduli spaces
2208:{\displaystyle \sigma }
1709:{\displaystyle E_{X/Y}}
1674:{\displaystyle C_{X/Y}}
900:of the cokernel bundle
825:). This is the case if
518:the class of a line in
2885:: CS1 maint: others (
2810:10.3842/SIGMA.2020.026
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1021:{\displaystyle E|_{X}}
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726:{\displaystyle E\to Y}
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374:{\displaystyle \beta }
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3030:) CS1 maint: others (
2716:Brambila-Paz, Leticia
2696:Chow group of a stack
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778:{\displaystyle (n-r)}
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267:rational curves on a
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2925:. pp. 282–333.
2722:. pp. 282–333.
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598:Geometric motivation
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273:Gromov–Witten theory
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124:enumerative geometry
40:improve this article
3117:Intersection theory
3072:Intersection Theory
2802:2020SIGMA..16..026B
2776:Manolache, Cristina
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2215:is the map given by
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1591:obstruction bundle
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271:. For example, in
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3082:978-1-4612-1700-8
3005:978-1-4704-5014-4
2679:{\displaystyle X}
2659:{\displaystyle Y}
2574:{\displaystyle Y}
2497:
2443:{\displaystyle 0}
2109:
2038:
1987:
1942:{\displaystyle X}
1729:{\displaystyle X}
1545:{\displaystyle Y}
1525:{\displaystyle X}
1379:act similarly to
1226:
1204:
1134:{\displaystyle X}
1081:{\displaystyle Y}
1061:{\displaystyle X}
1041:{\displaystyle s}
986:{\displaystyle Y}
966:{\displaystyle X}
946:{\displaystyle X}
858:{\displaystyle s}
838:{\displaystyle s}
818:{\displaystyle Y}
798:{\displaystyle n}
746:{\displaystyle X}
700:{\displaystyle r}
680:{\displaystyle s}
660:{\displaystyle Y}
616:{\displaystyle X}
511:{\displaystyle H}
438:
354:{\displaystyle X}
299:
269:quintic threefold
260:{\displaystyle d}
187:{\displaystyle X}
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1367:
1355:
1354:
1335:
1333:
1332:
1327:
1319:
1318:
1313:
1312:
1302:
1301:
1289:
1288:
1276:
1275:
1270:
1269:
1243:
1241:
1240:
1235:
1227:
1224:
1219:
1218:
1213:
1192:
1191:
1190:
1185:
1179:
1178:
1166:
1165:
1140:
1138:
1137:
1132:
1120:
1118:
1117:
1112:
1087:
1085:
1084:
1079:
1067:
1065:
1064:
1059:
1047:
1045:
1044:
1039:
1027:
1025:
1024:
1019:
1017:
1016:
1011:
992:
990:
989:
984:
972:
970:
969:
964:
952:
950:
949:
944:
932:
930:
929:
924:
922:
914:
895:
893:
892:
887:
879:
864:
862:
861:
856:
844:
842:
841:
836:
824:
822:
821:
816:
804:
802:
801:
796:
784:
782:
781:
776:
752:
750:
749:
744:
732:
730:
729:
724:
706:
704:
703:
698:
686:
684:
683:
678:
666:
664:
663:
658:
646:
644:
643:
638:
636:
635:
622:
620:
619:
614:
590:
588:
587:
582:
580:
579:
574:
546:
544:
543:
538:
536:
535:
530:
517:
515:
514:
509:
494:
492:
491:
486:
466:
465:
460:
451:
450:
439:
434:
429:
416:
414:
413:
408:
397:
396:
380:
378:
377:
372:
360:
358:
357:
352:
337:
335:
334:
329:
312:
311:
300:
295:
290:
266:
264:
263:
258:
241:
239:
238:
233:
222:
221:
193:
191:
190:
185:
173:
171:
170:
165:
162:
159:
157:
156:
155:
111:
104:
100:
97:
91:
89:
48:
24:
16:
3132:
3131:
3127:
3126:
3125:
3123:
3122:
3121:
3107:
3106:
3098:
3083:
3068:
3067:
3060:
3044:
3043:
3039:
3018:
3006:
2992:
2991:
2987:
2971:
2970:
2966:
2951:
2920:
2919:
2915:
2899:
2898:
2894:
2877:
2865:
2854:Mirror symmetry
2851:
2850:
2846:
2830:
2829:
2825:
2773:
2772:
2763:
2748:
2713:
2712:
2708:
2704:
2692:
2668:
2667:
2648:
2647:
2618:
2597:
2592:
2591:
2587:
2563:
2562:
2508:
2475:
2459:
2458:
2432:
2431:
2395:
2382:
2354:
2341:
2336:
2335:
2296:
2286:
2285:
2249:
2220:
2219:
2197:
2196:
2160:
2150:
2149:
2110:
2083:
2052:
2039:
2027:
2001:
1988:
1959:
1954:
1953:
1931:
1930:
1897:
1892:
1891:
1870:
1851:
1846:
1845:
1818:
1798:
1788:
1746:
1741:
1740:
1718:
1717:
1688:
1683:
1682:
1653:
1648:
1647:
1609:
1598:
1597:
1556:
1555:
1534:
1533:
1514:
1513:
1510:
1490:
1460:
1443:
1438:
1437:
1414:
1396:
1386:
1381:
1380:
1359:
1346:
1341:
1340:
1306:
1293:
1280:
1263:
1252:
1251:
1208:
1180:
1170:
1157:
1146:
1145:
1123:
1122:
1091:
1090:
1070:
1069:
1050:
1049:
1030:
1029:
1006:
998:
997:
975:
974:
955:
954:
935:
934:
915:
902:
901:
872:
867:
866:
847:
846:
827:
826:
807:
806:
787:
786:
755:
754:
735:
734:
709:
708:
689:
688:
669:
668:
649:
648:
625:
624:
605:
604:
600:
569:
552:
551:
525:
520:
519:
500:
499:
455:
427:
422:
421:
388:
383:
382:
363:
362:
343:
342:
288:
283:
282:
249:
248:
213:
196:
195:
176:
175:
147:
131:
130:
122:, specifically
112:
101:
95:
92:
49:
47:
37:
25:
12:
11:
5:
3130:
3128:
3120:
3119:
3109:
3108:
3105:
3104:
3097:
3096:
3081:
3058:
3037:
3004:
2985:
2964:
2949:
2913:
2892:
2863:
2844:
2838:hep-th/9405035
2823:
2761:
2746:
2705:
2703:
2700:
2699:
2698:
2691:
2688:
2675:
2655:
2633:
2629:
2625:
2621:
2617:
2612:
2608:
2604:
2600:
2586:
2583:
2570:
2547:
2544:
2541:
2538:
2535:
2530:
2523:
2519:
2515:
2511:
2506:
2502:
2490:
2486:
2482:
2478:
2473:
2469:
2466:
2439:
2415:
2410:
2406:
2402:
2398:
2394:
2389:
2385:
2381:
2378:
2375:
2372:
2367:
2364:
2361:
2357:
2353:
2348:
2344:
2318:
2311:
2307:
2303:
2299:
2294:
2270:
2267:
2262:
2259:
2256:
2252:
2248:
2245:
2242:
2239:
2236:
2233:
2230:
2227:
2204:
2182:
2175:
2171:
2167:
2163:
2158:
2134:
2131:
2128:
2123:
2120:
2117:
2113:
2105:
2098:
2094:
2090:
2086:
2081:
2076:
2072:
2067:
2063:
2059:
2055:
2051:
2046:
2042:
2034:
2030:
2025:
2021:
2016:
2012:
2008:
2004:
2000:
1995:
1991:
1985:
1981:
1977:
1974:
1971:
1966:
1962:
1938:
1916:
1912:
1908:
1902:
1890:for the ideal
1877:
1873:
1869:
1866:
1863:
1858:
1854:
1830:
1825:
1821:
1817:
1814:
1809:
1803:
1795:
1791:
1785:
1780:
1777:
1774:
1770:
1766:
1761:
1757:
1753:
1749:
1725:
1703:
1699:
1695:
1691:
1668:
1664:
1660:
1656:
1632:
1629:
1624:
1620:
1616:
1612:
1608:
1605:
1575:
1572:
1569:
1566:
1563:
1541:
1521:
1509:
1506:
1489:
1486:
1471:
1465:
1459:
1454:
1448:
1423:
1418:
1413:
1410:
1405:
1400:
1393:
1389:
1366:
1362:
1358:
1353:
1349:
1325:
1322:
1317:
1311:
1305:
1300:
1296:
1292:
1287:
1283:
1279:
1274:
1268:
1262:
1259:
1233:
1230:
1222:
1217:
1212:
1207:
1202:
1199:
1195:
1189:
1184:
1177:
1173:
1169:
1164:
1160:
1156:
1153:
1130:
1110:
1107:
1104:
1101:
1098:
1077:
1057:
1037:
1015:
1010:
1005:
982:
962:
942:
921:
918:
913:
909:
885:
882:
878:
875:
854:
834:
814:
794:
774:
771:
768:
765:
762:
742:
722:
719:
716:
707:vector bundle
696:
676:
656:
634:
612:
599:
596:
578:
573:
568:
565:
562:
559:
534:
529:
507:
484:
481:
478:
475:
472:
469:
464:
459:
454:
449:
446:
443:
437:
433:
406:
403:
400:
395:
391:
370:
350:
327:
324:
321:
318:
315:
310:
307:
304:
298:
294:
256:
231:
228:
225:
220:
216:
212:
209:
206:
203:
183:
154:
150:
145:
141:
138:
114:
113:
28:
26:
19:
13:
10:
9:
6:
4:
3:
2:
3129:
3118:
3115:
3114:
3112:
3103:
3100:
3099:
3092:
3088:
3084:
3078:
3074:
3073:
3065:
3063:
3059:
3053:
3048:
3041:
3038:
3033:
3029:
3023:
3015:
3011:
3007:
3001:
2997:
2996:
2989:
2986:
2980:
2975:
2968:
2965:
2960:
2956:
2952:
2950:9781107636385
2946:
2942:
2938:
2933:
2928:
2924:
2923:Moduli Spaces
2917:
2914:
2908:
2903:
2896:
2893:
2888:
2882:
2874:
2870:
2866:
2864:0-8218-2955-6
2860:
2856:
2855:
2848:
2845:
2839:
2834:
2827:
2824:
2819:
2815:
2811:
2807:
2803:
2799:
2794:
2789:
2785:
2781:
2777:
2770:
2768:
2766:
2762:
2757:
2753:
2749:
2747:9781107279544
2743:
2739:
2735:
2730:
2725:
2721:
2720:Moduli Spaces
2717:
2710:
2707:
2701:
2697:
2694:
2693:
2689:
2687:
2673:
2653:
2631:
2627:
2623:
2619:
2615:
2610:
2606:
2602:
2598:
2584:
2582:
2568:
2558:
2539:
2528:
2521:
2517:
2513:
2509:
2504:
2500:
2488:
2484:
2480:
2476:
2467:
2455:
2453:
2437:
2427:
2408:
2404:
2400:
2396:
2387:
2383:
2373:
2365:
2362:
2359:
2355:
2351:
2346:
2342:
2332:
2316:
2309:
2305:
2301:
2297:
2292:
2281:
2265:
2260:
2257:
2254:
2250:
2243:
2234:
2225:
2216:
2202:
2180:
2173:
2169:
2165:
2161:
2156:
2145:
2129:
2121:
2118:
2115:
2111:
2103:
2096:
2092:
2088:
2084:
2079:
2074:
2065:
2061:
2057:
2053:
2044:
2040:
2032:
2028:
2023:
2014:
2010:
2006:
2002:
1993:
1989:
1983:
1979:
1972:
1964:
1960:
1950:
1936:
1914:
1910:
1906:
1875:
1871:
1867:
1864:
1861:
1856:
1852:
1841:
1823:
1819:
1815:
1807:
1793:
1789:
1783:
1778:
1775:
1772:
1768:
1764:
1759:
1755:
1751:
1747:
1737:
1723:
1701:
1697:
1693:
1689:
1666:
1662:
1658:
1654:
1643:
1630:
1622:
1618:
1614:
1610:
1606:
1603:
1594:
1592:
1586:
1573:
1567:
1564:
1561:
1552:
1539:
1519:
1507:
1505:
1503:
1499:
1495:
1487:
1485:
1469:
1457:
1452:
1421:
1411:
1408:
1403:
1391:
1387:
1364:
1360:
1356:
1351:
1347:
1336:
1323:
1315:
1298:
1294:
1285:
1281:
1272:
1257:
1248:
1244:
1231:
1215:
1205:
1200:
1197:
1193:
1187:
1175:
1171:
1162:
1158:
1151:
1142:
1128:
1108:
1102:
1099:
1096:
1075:
1055:
1035:
1013:
1003:
994:
980:
960:
940:
919:
916:
911:
907:
899:
883:
880:
876:
873:
852:
832:
812:
792:
769:
766:
763:
740:
720:
714:
694:
674:
667:by a section
654:
610:
597:
595:
591:
576:
563:
560:
557:
548:
532:
505:
495:
476:
470:
467:
462:
447:
444:
441:
418:
401:
393:
389:
368:
361:a scheme and
348:
338:
322:
319:
316:
308:
305:
302:
279:
278:
274:
270:
254:
245:
226:
218:
214:
210:
204:
181:
152:
148:
139:
129:
125:
121:
110:
107:
99:
88:
85:
81:
78:
74:
71:
67:
64:
60:
57: –
56:
52:
51:Find sources:
45:
41:
35:
34:
29:This article
27:
23:
18:
17:
3071:
3040:
2994:
2988:
2979:math/0509076
2967:
2922:
2916:
2907:math/9806111
2895:
2853:
2847:
2826:
2783:
2779:
2719:
2709:
2588:
2560:
2457:
2451:
2429:
2334:
2283:
2218:
2147:
1952:
1843:
1739:
1681:embeds into
1645:
1596:
1590:
1588:
1554:
1511:
1491:
1338:
1250:
1246:
1144:
1121:cutting out
995:
601:
593:
550:
497:
420:
340:
281:
127:
117:
102:
93:
83:
76:
69:
62:
50:
38:Please help
33:verification
30:
2590:would give
898:Euler class
381:a class in
174:of a space
120:mathematics
96:August 2021
3014:1080251406
2793:1804.06048
2702:References
1496:using the
687:of a rank-
66:newspapers
3091:958523758
3022:cite book
2959:117183792
2932:1111.1552
2881:cite book
2818:119167258
2756:117183792
2729:1111.1552
2616:≅
2380:→
2363:−
2347:∗
2343:π
2258:∩
2226:σ
2203:σ
2119:−
2116:∗
2045:∗
2033:∗
1994:∗
1984:σ
1965:∗
1865:…
1816:−
1794:∗
1769:⨁
1628:→
1604:π
1571:↪
1321:→
1304:→
1291:→
1278:→
1261:→
1229:→
1221:→
1168:→
1155:→
1106:→
881:⊂
767:−
718:→
567:→
436:¯
369:β
323:β
297:¯
244:Chow ring
219:∗
211:∈
153:∙
3111:Category
2873:52374327
2690:See also
2195:, where
2148:denoted
2075:→
2024:→
1980:→
1194:→
920:′
877:′
2798:Bibcode
2786:: 026.
785:(where
733:. Then
242:in its
80:scholar
3089:
3079:
3012:
3002:
2957:
2947:
2871:
2861:
2816:
2754:
2744:
1500:and a
1339:where
275:, the
126:, the
82:
75:
68:
61:
53:
3047:arXiv
2974:arXiv
2955:S2CID
2927:arXiv
2902:arXiv
2833:arXiv
2814:S2CID
2788:arXiv
2752:S2CID
2724:arXiv
1716:over
933:over
87:JSTOR
73:books
3087:OCLC
3077:ISBN
3032:link
3028:link
3010:OCLC
3000:ISBN
2945:ISBN
2887:link
2869:OCLC
2859:ISBN
2742:ISBN
2284:and
1436:and
498:for
341:for
59:news
2937:doi
2806:doi
2734:doi
2496:vir
973:in
160:vir
118:In
42:by
3113::
3085:.
3061:^
3024:}}
3020:{{
3008:.
2953:.
2943:.
2935:.
2883:}}
2879:{{
2867:.
2812:.
2804:.
2796:.
2784:16
2782:.
2764:^
2750:.
2740:.
2732:.
2686:.
2581:.
2501::=
1225:ob
993:.
3093:.
3055:.
3049::
3034:)
3016:.
2982:.
2976::
2961:.
2939::
2929::
2910:.
2904::
2889:)
2875:.
2841:.
2835::
2820:.
2808::
2800::
2790::
2758:.
2736::
2726::
2674:X
2654:Y
2632:Y
2628:/
2624:X
2620:N
2611:Y
2607:/
2603:X
2599:C
2569:Y
2546:)
2543:]
2540:Y
2537:[
2534:(
2529:!
2522:Y
2518:/
2514:X
2510:E
2505:f
2489:Y
2485:/
2481:X
2477:E
2472:]
2468:X
2465:[
2438:0
2426:.
2414:)
2409:Y
2405:/
2401:X
2397:E
2393:(
2388:k
2384:A
2377:)
2374:X
2371:(
2366:r
2360:k
2356:A
2352::
2317:!
2310:Y
2306:/
2302:X
2298:E
2293:0
2269:]
2266:V
2261:X
2255:V
2251:C
2247:[
2244:=
2241:)
2238:]
2235:V
2232:[
2229:(
2181:!
2174:Y
2170:/
2166:X
2162:E
2157:f
2133:)
2130:X
2127:(
2122:r
2112:A
2104:!
2097:Y
2093:/
2089:X
2085:E
2080:0
2071:)
2066:Y
2062:/
2058:X
2054:E
2050:(
2041:A
2029:i
2020:)
2015:Y
2011:/
2007:X
2003:C
1999:(
1990:A
1976:)
1973:Y
1970:(
1961:A
1937:X
1915:Y
1911:/
1907:X
1901:I
1876:r
1872:f
1868:,
1862:,
1857:1
1853:f
1829:)
1824:j
1820:D
1813:(
1808:Y
1802:O
1790:i
1784:r
1779:1
1776:=
1773:j
1765:=
1760:Y
1756:/
1752:X
1748:E
1724:X
1702:Y
1698:/
1694:X
1690:E
1667:Y
1663:/
1659:X
1655:C
1631:X
1623:Y
1619:/
1615:X
1611:E
1607::
1593:)
1574:Y
1568:X
1565::
1562:i
1540:Y
1520:X
1470:2
1464:T
1458:,
1453:1
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1422:X
1417:|
1412:E
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1399:|
1392:Y
1388:T
1365:2
1361:E
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1348:E
1324:0
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1310:T
1299:2
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1286:1
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1258:0
1232:0
1216:X
1211:|
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1100::
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1056:X
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1009:|
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981:Y
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912:/
908:E
884:E
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853:s
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813:Y
793:n
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770:r
764:n
761:(
741:X
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695:r
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577:2
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564:C
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506:H
483:)
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474:[
471:1
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394:1
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320:,
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314:(
309:n
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303:g
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255:d
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227:X
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215:A
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205:X
202:[
182:X
149:E
144:]
140:X
137:[
109:)
103:(
98:)
94:(
84:·
77:·
70:·
63:·
36:.
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