517:
331:
351:
754:, surfaces that can't be obtained from another by blowing up at a point; they have no connection with the minimal surfaces of differential geometry
490:, the locus of lines that lie on at least two quadrics in a general three dimensional linear system of quadric surfaces in projective 3-space
821:
25:
917:
859:
846:
109:
103:
410:
538:
912:
811:, surfaces in finite characteristic that admit a purely inseparable dominant rational map from the projective plane
907:
805:
of some other surface by the action of a finite group; examples include Kummer, Godeaux, Hopf, and Inoue surfaces
725:
230:
473:
689:
586:
704:
699:
135:
751:
632:
556:
206:
180:
493:
732:
Exceptional surfaces, surfaces whose Picard number achieve the bound set by the central Hodge number
622:
155:
724:
and generalized
Raynaud surfaces, certain quasielliptic counterexamples to the conclusions of the
537:, surfaces of degree 10 in projective 4-space that are the zero locus of sections of the rank-two
741:, complex surfaces with a Kähler metric; equivalently, surfaces for which the first Betti number
609:
294:
282:
260:
738:
455:
855:
842:
769:
683:
599:
578:
371:
254:
224:
166:
21:
17:
872:
826:
711:
665:
627:
550:
480:
278:
272:
236:
202:
140:
44:
37:
808:
787:
721:
694:
670:
652:
649:
of lines on a non-singular 3-fold; sometimes, this term is taken to mean del Pezzo surface
604:
566:
527:
487:
468:
356:
219:
215:
148:
114:
58:
51:
594:
461:
436:
336:
553:, a variation on the notion of Enriques surfaces that only exist in characteristic two
901:
885:
793:
775:
757:
636:
405:
390:
288:
266:
249:
176:
160:
125:
96:
781:
656:
646:
640:
613:
447:
441:
415:
399:
393:; several other families discovered by Inoue have also been called "Inoue surfaces"
385:
379:
210:
184:
120:
802:
73:
563:
are a variation of this notion that exist only in characteristics two and three
429:
78:
68:
20:, compact complex surfaces, and families thereof, sorted according to their
718:
constitute a modification this idea that occurs in finite characteristic
88:
63:
894:
to visualize algebraic surfaces in real-time, including a user gallery.
891:
841:
by Wolf P. Barth, Klaus Hulek, Chris A.M. Peters, Antonius Van de Ven
778:, referring to a certain sextic with 65 nodes and decic with 345 nodes
171:
130:
83:
192:, surfaces of revolution generated by a circle about a coplanar axis
879:
189:
522:
The quotient of a K3 surface under a fixpointfree involution.
359:, the White surfaces determined by families of quartic curves
163:, inversions of a cylinder, torus, or double cone in a sphere
801:
Quotient surfaces, surfaces that are constructed as the
677:
Families of surfaces with members in multiple classes
496:
339:
297:
269:, intersections of two quadrics in projective 4-space
511:
345:
325:
239:, a family of minimal surfaces of variable degree
796:, a certain surface of degree 12 with 600 nodes
766:Kummer surfaces, quartic surfaces with 16 nodes
285:of the projective plane into projective 5-space
790:, a certain surface of degree 8 with 168 nodes
760:, surfaces whose only singularities are nodes
257:, surfaces with an ample anticanonical divisor
8:
643:as projective plane but not isomorphic to it
655:; surfaces of general type with the same
612:; surfaces of general type with the same
503:
499:
498:
495:
338:
317:
301:
296:
291:, the blow-up of the projective plane at
179:or Steiner surface, a realization of the
888:of algebraic surfaces by Herwig Hauser.
763:Cayley's nodal cubic, which has 4 nodes
714:, surfaces with an elliptic fibration;
333:points by the linear system of degree-
106:, a certain cubic surface with 4 nodes
545:Other classes of dimension-0 surfaces
7:
244:Other families of rational surfaces
882:, especially ones with many nodes.
616:as Campedelli surfaces are called
14:
772:, a certain quintic with 31 nodes
639:surfaces, surfaces with the same
784:, a certain septic with 99 nodes
512:{\displaystyle \mathbb {P} ^{3}}
227:, a minimal surface of degree 15
197:Other rational surfaces in space
822:EnriquesâKodaira classification
659:as Godeaux surfaces are called
551:Non-classical Enriques surfaces
464:, birational to Kummer surfaces
458:, birational to Kummer surfaces
26:EnriquesâKodaira classification
880:pictures of algebraic surfaces
205:, a sextic realization of the
1:
871:Mathworld has a long list of
618:numerical Campidelli surfaces
561:quasi-hyperelliptic surfaces
353:curves through those points
117:or Klein icosahedral surface
110:Cayley's ruled cubic surface
366:Non-rational ruled surfaces
326:{\displaystyle _{n+1}C_{2}}
934:
852:Complex algebraic surfaces
661:numerical Godeaux surfaces
104:Cayley nodal cubic surface
918:Mathematics-related lists
726:Kodaira vanishing theorem
535:HorrocksâMumford surfaces
474:Supersingular K3 surfaces
444:, special Kummer surfaces
411:InoueâHirzebruch surfaces
263:, rational ruled surfaces
839:Compact Complex Surfaces
690:Hilbert modular surfaces
587:surfaces of general type
559:or bielliptic surfaces;
450:, a special tetrahedroid
233:, a surface of degree 16
16:This is a list of named
705:Shioda modular surfaces
700:Picard modular surfaces
682:Surfaces that are also
539:HorrocksâMumford bundle
716:quasielliptic surfaces
633:Fake projective planes
557:Hyperelliptic surfaces
513:
347:
327:
231:Bour's minimal surface
854:by Arnaud Beauville,
585:Kodaira dimension 2 (
514:
348:
328:
207:real projective plane
181:real projective plane
172:Right circular conoid
623:Castelnuovo surfaces
494:
337:
295:
273:Unirational surfaces
32:Kodaira dimension ââ
892:Free program SURFER
610:Campedelli surfaces
573:Kodaira dimension 1
424:Kodaira dimension 0
275:of characteristic 0
261:Hirzebruch surfaces
913:Algebraic surfaces
873:algebraic surfaces
600:Beauville surfaces
579:Dolgachev surfaces
509:
372:Class VII surfaces
343:
323:
283:Veronese embedding
255:Del Pezzo surfaces
18:algebraic surfaces
770:Togliatti surface
712:Elliptic surfaces
684:Shimura varieties
666:Horikawa surfaces
628:Catanese surfaces
481:Enriques surfaces
378:Vanishing second
346:{\displaystyle n}
237:Richmond surfaces
225:Henneberg surface
156:Châtelet surfaces
38:Rational surfaces
22:Kodaira dimension
925:
908:Complex surfaces
827:List of surfaces
809:Zariski surfaces
752:Minimal surfaces
722:Raynaud surfaces
695:Humbert surfaces
671:Todorov surfaces
653:Godeaux surfaces
605:Burniat surfaces
567:Kodaira surfaces
528:Abelian surfaces
518:
516:
515:
510:
508:
507:
502:
488:Reye congruences
469:quartic surfaces
456:PlĂźcker surfaces
398:Positive second
357:Bordiga surfaces
352:
350:
349:
344:
332:
330:
329:
324:
322:
321:
312:
311:
279:Veronese surface
149:quartic surfaces
141:Whitney umbrella
136:PlĂźcker's conoid
131:Parabolic conoid
52:Quadric surfaces
45:Projective plane
933:
932:
928:
927:
926:
924:
923:
922:
898:
897:
868:
835:
818:
788:Endrass surface
747:
739:Kähler surfaces
679:
595:Barlow surfaces
591:
575:
547:
531:
497:
492:
491:
484:
462:Weddle surfaces
437:Kummer surfaces
433:
426:
375:
368:
335:
334:
313:
298:
293:
292:
246:
220:minimal surface
216:Enneper surface
199:
152:
115:Clebsch surface
100:
59:Cone (geometry)
55:
41:
34:
12:
11:
5:
931:
929:
921:
920:
915:
910:
900:
899:
896:
895:
889:
883:
876:
875:with pictures.
867:
866:External links
864:
863:
862:
849:
834:
831:
830:
829:
824:
817:
814:
813:
812:
806:
799:
798:
797:
791:
785:
779:
776:Barth surfaces
773:
767:
764:
758:Nodal surfaces
755:
749:
745:
736:
730:
729:
728:
709:
708:
707:
702:
697:
692:
678:
675:
674:
673:
668:
663:
650:
644:
630:
625:
620:
607:
602:
597:
590:
583:
582:
581:
574:
571:
570:
569:
564:
554:
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542:
541:
530:
525:
524:
523:
520:
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483:
478:
477:
476:
471:
465:
459:
453:
452:
451:
445:
432:
427:
425:
422:
421:
420:
419:
418:
413:
408:
406:Enoki surfaces
396:
395:
394:
391:Inoue surfaces
388:
374:
369:
367:
364:
363:
362:
361:
360:
342:
320:
316:
310:
307:
304:
300:
289:White surfaces
286:
276:
270:
267:Segre surfaces
264:
258:
252:
250:Coble surfaces
245:
242:
241:
240:
234:
228:
222:
213:
198:
195:
194:
193:
187:
174:
169:
167:Gabriel's horn
164:
161:Dupin cyclides
158:
151:
145:
144:
143:
138:
133:
128:
123:
118:
112:
107:
99:
97:cubic surfaces
93:
92:
91:
86:
81:
76:
71:
66:
61:
54:
49:
48:
47:
40:
35:
33:
30:
13:
10:
9:
6:
4:
3:
2:
930:
919:
916:
914:
911:
909:
906:
905:
903:
893:
890:
887:
884:
881:
877:
874:
870:
869:
865:
861:
860:0-521-28815-0
857:
853:
850:
848:
847:3-540-00832-2
844:
840:
837:
836:
832:
828:
825:
823:
820:
819:
815:
810:
807:
804:
800:
795:
794:Sarti surface
792:
789:
786:
783:
780:
777:
774:
771:
768:
765:
762:
761:
759:
756:
753:
750:
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731:
727:
723:
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693:
691:
688:
687:
685:
681:
680:
676:
672:
669:
667:
664:
662:
658:
657:Hodge numbers
654:
651:
648:
645:
642:
641:Betti numbers
638:
634:
631:
629:
626:
624:
621:
619:
615:
614:Hodge numbers
611:
608:
606:
603:
601:
598:
596:
593:
592:
588:
584:
580:
577:
576:
572:
568:
565:
562:
558:
555:
552:
549:
548:
544:
540:
536:
533:
532:
529:
526:
521:
504:
489:
486:
485:
482:
479:
475:
472:
470:
466:
463:
460:
457:
454:
449:
446:
443:
442:Tetrahedroids
440:
439:
438:
435:
434:
431:
428:
423:
417:
416:Kato surfaces
414:
412:
409:
407:
404:
403:
401:
397:
392:
389:
387:
386:Hopf surfaces
384:
383:
381:
377:
376:
373:
370:
365:
358:
355:
354:
340:
318:
314:
308:
305:
302:
299:
290:
287:
284:
280:
277:
274:
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247:
243:
238:
235:
232:
229:
226:
223:
221:
217:
214:
212:
208:
204:
203:Boy's surface
201:
200:
196:
191:
188:
186:
182:
178:
177:Roman surface
175:
173:
170:
168:
165:
162:
159:
157:
154:
153:
150:
146:
142:
139:
137:
134:
132:
129:
127:
126:Monkey saddle
124:
122:
119:
116:
113:
111:
108:
105:
102:
101:
98:
94:
90:
87:
85:
82:
80:
77:
75:
72:
70:
67:
65:
62:
60:
57:
56:
53:
50:
46:
43:
42:
39:
36:
31:
29:
27:
23:
19:
851:
838:
782:Labs surface
742:
733:
715:
660:
647:Fano surface
617:
560:
534:
448:Wave surface
400:Betti number
380:Betti number
211:affine space
185:affine space
121:Fermat cubic
15:
803:orbit space
430:K3 surfaces
74:Hyperboloid
902:Categories
878:Some more
833:References
218:, a nonic
79:Paraboloid
24:following
147:Rational
95:Rational
69:Ellipsoid
886:Pictures
816:See also
209:in real
183:in real
89:Spheroid
64:Cylinder
748:is even
637:Mumford
467:Smooth
858:
845:
281:, the
84:Sphere
856:ISBN
843:ISBN
190:Tori
635:or
904::
686::
402::
382::
28:.
746:1
743:b
734:h
589:)
519:.
505:3
500:P
341:n
319:2
315:C
309:1
306:+
303:n
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