579:
454:
378:
245:
308:
477:
285:
265:
191:
163:
143:
119:
99:
68:
620:
644:
562:
389:
316:
613:
639:
554:
215:
71:
649:
606:
498:
194:
523:
558:
515:
79:
507:
493:
290:
43:
535:
531:
17:
590:
550:
489:
462:
270:
250:
202:
176:
166:
148:
128:
122:
104:
84:
75:
53:
39:
459:
This theorem applies in particular to any smooth, complex affine variety of dimension
633:
542:
31:
198:
519:
578:
586:
527:
511:
247:
is a closed connected complex submanifold of complex dimension
449:{\displaystyle H_{i}(V;\mathbb {Z} )=0,{\text{ for }}i>n.}
373:{\displaystyle H^{i}(V;\mathbb {Z} )=0,{\text{ for }}i>n}
496:(1959), "The Lefschetz theorem on hyperplane sections",
287:
has the homotopy type of a CW complex of real dimension
594:
465:
392:
319:
293:
273:
253:
218:
179:
151:
131:
107:
87:
56:
549:. Annals of Mathematics Studies, No. 51. Notes by
471:
448:
372:
302:
279:
259:
239:
185:
157:
137:
113:
93:
62:
47:
614:
8:
240:{\displaystyle V\subseteq \mathbb {C} ^{r}}
621:
607:
464:
429:
413:
412:
397:
391:
356:
340:
339:
324:
318:
292:
272:
252:
231:
227:
226:
217:
178:
150:
130:
106:
86:
55:
27:Mathematical theorem of complex manifolds
169:with critical points of index at most
7:
575:
573:
25:
553:and Robert Wells. Princeton, NJ:
577:
417:
403:
344:
330:
1:
593:. You can help Knowledge by
645:Theorems in homotopy theory
666:
572:
555:Princeton University Press
36:Andreotti–Frankel theorem
18:Andreotti-Frankel theorem
101:or, more generally, if
473:
450:
374:
304:
303:{\displaystyle \leq n}
281:
261:
241:
187:
159:
139:
115:
95:
64:
499:Annals of Mathematics
474:
451:
375:
305:
282:
262:
242:
188:
160:
140:
116:
96:
65:
463:
390:
317:
291:
271:
251:
216:
177:
149:
129:
105:
85:
54:
195:homotopy equivalent
469:
446:
370:
300:
277:
257:
237:
183:
155:
135:
111:
91:
60:
50:), states that if
40:Aldo Andreotti
640:Complex manifolds
602:
601:
502:, Second Series,
494:Frankel, Theodore
472:{\displaystyle n}
432:
359:
280:{\displaystyle V}
260:{\displaystyle n}
212:Consequently, if
186:{\displaystyle V}
158:{\displaystyle V}
138:{\displaystyle n}
114:{\displaystyle V}
94:{\displaystyle n}
80:complex dimension
63:{\displaystyle V}
16:(Redirected from
657:
623:
616:
609:
587:topology-related
581:
574:
568:
538:
478:
476:
475:
470:
455:
453:
452:
447:
433:
430:
416:
402:
401:
379:
377:
376:
371:
360:
357:
343:
329:
328:
309:
307:
306:
301:
286:
284:
283:
278:
266:
264:
263:
258:
246:
244:
243:
238:
236:
235:
230:
192:
190:
189:
184:
164:
162:
161:
156:
144:
142:
141:
136:
120:
118:
117:
112:
100:
98:
97:
92:
69:
67:
66:
61:
44:Theodore Frankel
38:, introduced by
21:
665:
664:
660:
659:
658:
656:
655:
654:
630:
629:
628:
627:
565:
543:Milnor, John W.
541:
512:10.2307/1970034
490:Andreotti, Aldo
488:
485:
461:
460:
431: for
393:
388:
387:
358: for
320:
315:
314:
289:
288:
269:
268:
249:
248:
225:
214:
213:
175:
174:
147:
146:
127:
126:
103:
102:
83:
82:
52:
51:
28:
23:
22:
15:
12:
11:
5:
663:
661:
653:
652:
650:Topology stubs
647:
642:
632:
631:
626:
625:
618:
611:
603:
600:
599:
582:
571:
570:
563:
551:Michael Spivak
539:
484:
481:
468:
457:
456:
445:
442:
439:
436:
428:
425:
422:
419:
415:
411:
408:
405:
400:
396:
381:
380:
369:
366:
363:
355:
352:
349:
346:
342:
338:
335:
332:
327:
323:
299:
296:
276:
256:
234:
229:
224:
221:
203:real dimension
182:
167:Morse function
154:
134:
123:Stein manifold
110:
90:
76:affine variety
59:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
662:
651:
648:
646:
643:
641:
638:
637:
635:
624:
619:
617:
612:
610:
605:
604:
598:
596:
592:
589:article is a
588:
583:
580:
576:
566:
564:0-691-08008-9
560:
556:
552:
548:
544:
540:
537:
533:
529:
525:
521:
517:
513:
509:
505:
501:
500:
495:
491:
487:
486:
482:
480:
466:
443:
440:
437:
434:
426:
423:
420:
409:
406:
398:
394:
386:
385:
384:
367:
364:
361:
353:
350:
347:
336:
333:
325:
321:
313:
312:
311:
297:
294:
274:
254:
232:
222:
219:
210:
208:
204:
200:
196:
180:
172:
168:
152:
132:
125:of dimension
124:
108:
88:
81:
77:
73:
57:
49:
45:
42: and
41:
37:
33:
19:
595:expanding it
584:
547:Morse theory
546:
503:
497:
458:
382:
310:. Therefore
211:
206:
170:
35:
29:
506:: 713–717,
32:mathematics
634:Categories
569:Chapter 7.
483:References
199:CW complex
74:, complex
520:0003-486X
295:≤
223:⊆
173:, and so
165:admits a
545:(1963).
205:at most
145:, then
536:0177422
528:1970034
267:, then
121:is any
46: (
561:
534:
526:
518:
72:smooth
34:, the
585:This
524:JSTOR
197:to a
70:is a
591:stub
559:ISBN
516:ISSN
438:>
383:and
365:>
48:1959
508:doi
209:.
201:of
193:is
78:of
30:In
636::
557:.
532:MR
530:,
522:,
514:,
504:69
492:;
479:.
622:e
615:t
608:v
597:.
567:.
510::
467:n
444:.
441:n
435:i
427:,
424:0
421:=
418:)
414:Z
410:;
407:V
404:(
399:i
395:H
368:n
362:i
354:,
351:0
348:=
345:)
341:Z
337:;
334:V
331:(
326:i
322:H
298:n
275:V
255:n
233:r
228:C
220:V
207:n
181:V
171:n
153:V
133:n
109:V
89:n
58:V
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
