528:
342:
362:
765:, 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
501:, 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
17:
832:
36:
928:
870:
857:
822:, surfaces in finite characteristic that admit a purely inseparable dominant rational map from the projective plane
816:
of some other surface by the action of a finite group; examples include Kummer, Godeaux, Hopf, and Inoue surfaces
120:
114:
421:
923:
549:
504:
918:
743:
Exceptional surfaces, surfaces whose Picard number achieve the bound set by the central Hodge number
736:
241:
484:
735:
and generalized
Raynaud surfaces, certain quasielliptic counterexamples to the conclusions of the
548:, surfaces of degree 10 in projective 4-space that are the zero locus of sections of the rank-two
283:
752:, complex surfaces with a Kähler metric; equivalently, surfaces for which the first Betti number
700:
597:
305:
715:
710:
146:
883:
762:
643:
567:
217:
191:
660:
of lines on a non-singular 3-fold; sometimes, this term is taken to mean del Pezzo surface
8:
633:
166:
74:
620:
347:
293:
271:
749:
564:, a variation on the notion of Enriques surfaces that only exist in characteristic two
466:
896:
866:
853:
780:
694:
610:
589:
382:
265:
235:
182:
177:
32:
28:
837:
722:
676:
638:
561:
491:
404:; several other families discovered by Inoue have also been called "Inoue surfaces"
289:
247:
213:
151:
55:
48:
819:
798:
732:
705:
681:
663:
615:
577:
538:
498:
479:
367:
230:
226:
159:
125:
69:
62:
141:
605:
574:
are a variation of this notion that exist only in characteristics two and three
472:
447:
912:
804:
786:
768:
647:
416:
401:
299:
277:
260:
187:
171:
136:
107:
31:, compact complex surfaces, and families thereof, sorted according to their
792:
667:
657:
651:
624:
458:
452:
426:
410:
396:
390:
221:
195:
131:
813:
729:
constitute a modification this idea that occurs in finite characteristic
84:
687:
905:
to visualize algebraic surfaces in real-time, including a user gallery.
440:
89:
902:
852:
by Wolf P. Barth, Klaus Hulek, Chris A.M. Peters, Antonius Van de Ven
789:, referring to a certain sextic with 65 nodes and decic with 345 nodes
79:
203:, surfaces of revolution generated by a circle about a coplanar axis
99:
890:
595:
94:
533:
The quotient of a K3 surface under a fixpointfree involution.
370:, the White surfaces determined by families of quartic curves
200:
174:, inversions of a cylinder, torus, or double cone in a sphere
812:
Quotient surfaces, surfaces that are constructed as the
555:
254:
688:
Families of surfaces with members in multiple classes
507:
350:
308:
280:, intersections of two quadrics in projective 4-space
207:
522:
356:
336:
250:, a family of minimal surfaces of variable degree
910:
807:, a certain surface of degree 12 with 600 nodes
777:Kummer surfaces, quartic surfaces with 16 nodes
296:of the projective plane into projective 5-space
801:, a certain surface of degree 8 with 168 nodes
771:, surfaces whose only singularities are nodes
376:
268:, surfaces with an ample anticanonical divisor
654:as projective plane but not isomorphic to it
157:
105:
666:; surfaces of general type with the same
623:; surfaces of general type with the same
510:
302:, the blow-up of the projective plane at
190:or Steiner surface, a realization of the
899:of algebraic surfaces by Herwig Hauser.
774:Cayley's nodal cubic, which has 4 nodes
725:, surfaces with an elliptic fibration;
42:
14:
911:
583:
434:
344:points by the linear system of degree-
117:, a certain cubic surface with 4 nodes
556:Other classes of dimension-0 surfaces
381:
490:
47:
537:
255:Other families of rational surfaces
61:
24:
893:, especially ones with many nodes.
627:as Campedelli surfaces are called
25:
940:
876:
783:, a certain quintic with 31 nodes
650:surfaces, surfaces with the same
795:, a certain septic with 99 nodes
523:{\displaystyle \mathbb {P} ^{3}}
238:, a minimal surface of degree 15
208:Other rational surfaces in space
833:EnriquesâKodaira classification
670:as Godeaux surfaces are called
562:Non-classical Enriques surfaces
475:, birational to Kummer surfaces
469:, birational to Kummer surfaces
37:EnriquesâKodaira classification
891:pictures of algebraic surfaces
439:
216:, a sextic realization of the
13:
1:
882:Mathworld has a long list of
843:
629:numerical Campidelli surfaces
572:quasi-hyperelliptic surfaces
364:curves through those points
128:or Klein icosahedral surface
121:Cayley's ruled cubic surface
7:
826:
377:Non-rational ruled surfaces
337:{\displaystyle _{n+1}C_{2}}
10:
945:
863:Complex algebraic surfaces
672:numerical Godeaux surfaces
115:Cayley nodal cubic surface
18:List of algebraic surfaces
929:Mathematics-related lists
737:Kodaira vanishing theorem
546:HorrocksâMumford surfaces
485:Supersingular K3 surfaces
455:, special Kummer surfaces
422:InoueâHirzebruch surfaces
274:, rational ruled surfaces
850:Compact Complex Surfaces
701:Hilbert modular surfaces
598:surfaces of general type
570:or bielliptic surfaces;
461:, a special tetrahedroid
244:, a surface of degree 16
27:This is a list of named
716:Shioda modular surfaces
711:Picard modular surfaces
693:Surfaces that are also
550:HorrocksâMumford bundle
727:quasielliptic surfaces
644:Fake projective planes
568:Hyperelliptic surfaces
524:
358:
338:
242:Bour's minimal surface
865:by Arnaud Beauville,
596:Kodaira dimension 2 (
525:
359:
339:
218:real projective plane
192:real projective plane
183:Right circular conoid
634:Castelnuovo surfaces
505:
348:
306:
284:Unirational surfaces
43:Kodaira dimension ââ
903:Free program SURFER
621:Campedelli surfaces
584:Kodaira dimension 1
435:Kodaira dimension 0
286:of characteristic 0
272:Hirzebruch surfaces
924:Algebraic surfaces
884:algebraic surfaces
611:Beauville surfaces
590:Dolgachev surfaces
520:
383:Class VII surfaces
354:
334:
294:Veronese embedding
266:Del Pezzo surfaces
29:algebraic surfaces
781:Togliatti surface
723:Elliptic surfaces
695:Shimura varieties
677:Horikawa surfaces
639:Catanese surfaces
492:Enriques surfaces
389:Vanishing second
357:{\displaystyle n}
248:Richmond surfaces
236:Henneberg surface
167:Châtelet surfaces
49:Rational surfaces
33:Kodaira dimension
16:(Redirected from
936:
919:Complex surfaces
838:List of surfaces
820:Zariski surfaces
763:Minimal surfaces
733:Raynaud surfaces
706:Humbert surfaces
682:Todorov surfaces
664:Godeaux surfaces
616:Burniat surfaces
578:Kodaira surfaces
539:Abelian surfaces
529:
527:
526:
521:
519:
518:
513:
499:Reye congruences
480:quartic surfaces
467:PlĂźcker surfaces
409:Positive second
368:Bordiga surfaces
363:
361:
360:
355:
343:
341:
340:
335:
333:
332:
323:
322:
290:Veronese surface
160:quartic surfaces
152:Whitney umbrella
147:PlĂźcker's conoid
142:Parabolic conoid
63:Quadric surfaces
56:Projective plane
21:
944:
943:
939:
938:
937:
935:
934:
933:
909:
908:
879:
846:
829:
799:Endrass surface
758:
750:Kähler surfaces
690:
606:Barlow surfaces
602:
586:
558:
542:
514:
509:
508:
506:
503:
502:
495:
473:Weddle surfaces
448:Kummer surfaces
444:
437:
386:
379:
349:
346:
345:
328:
324:
312:
309:
307:
304:
303:
257:
231:minimal surface
227:Enneper surface
210:
163:
126:Clebsch surface
111:
70:Cone (geometry)
66:
52:
45:
23:
22:
15:
12:
11:
5:
942:
932:
931:
926:
921:
907:
906:
900:
894:
887:
886:with pictures.
878:
877:External links
875:
874:
873:
860:
845:
842:
841:
840:
835:
828:
825:
824:
823:
817:
810:
809:
808:
802:
796:
790:
787:Barth surfaces
784:
778:
775:
769:Nodal surfaces
766:
760:
756:
747:
741:
740:
739:
720:
719:
718:
713:
708:
703:
689:
686:
685:
684:
679:
674:
661:
655:
641:
636:
631:
618:
613:
608:
601:
594:
593:
592:
585:
582:
581:
580:
575:
565:
557:
554:
553:
552:
541:
536:
535:
534:
531:
517:
512:
494:
489:
488:
487:
482:
476:
470:
464:
463:
462:
456:
443:
438:
436:
433:
432:
431:
430:
429:
424:
419:
417:Enoki surfaces
407:
406:
405:
402:Inoue surfaces
399:
385:
380:
378:
375:
374:
373:
372:
371:
353:
331:
327:
321:
318:
315:
311:
300:White surfaces
297:
287:
281:
278:Segre surfaces
275:
269:
263:
261:Coble surfaces
256:
253:
252:
251:
245:
239:
233:
224:
209:
206:
205:
204:
198:
185:
180:
178:Gabriel's horn
175:
172:Dupin cyclides
169:
162:
156:
155:
154:
149:
144:
139:
134:
129:
123:
118:
110:
108:cubic surfaces
104:
103:
102:
97:
92:
87:
82:
77:
72:
65:
60:
59:
58:
51:
46:
44:
41:
9:
6:
4:
3:
2:
941:
930:
927:
925:
922:
920:
917:
916:
914:
904:
901:
898:
895:
892:
888:
885:
881:
880:
872:
871:0-521-28815-0
868:
864:
861:
859:
858:3-540-00832-2
855:
851:
848:
847:
839:
836:
834:
831:
830:
821:
818:
815:
811:
806:
805:Sarti surface
803:
800:
797:
794:
791:
788:
785:
782:
779:
776:
773:
772:
770:
767:
764:
761:
755:
751:
748:
746:
742:
738:
734:
731:
730:
728:
724:
721:
717:
714:
712:
709:
707:
704:
702:
699:
698:
696:
692:
691:
683:
680:
678:
675:
673:
669:
668:Hodge numbers
665:
662:
659:
656:
653:
652:Betti numbers
649:
645:
642:
640:
637:
635:
632:
630:
626:
625:Hodge numbers
622:
619:
617:
614:
612:
609:
607:
604:
603:
599:
591:
588:
587:
579:
576:
573:
569:
566:
563:
560:
559:
551:
547:
544:
543:
540:
532:
515:
500:
497:
496:
493:
486:
483:
481:
477:
474:
471:
468:
465:
460:
457:
454:
453:Tetrahedroids
451:
450:
449:
446:
445:
442:
428:
427:Kato surfaces
425:
423:
420:
418:
415:
414:
412:
408:
403:
400:
398:
397:Hopf surfaces
395:
394:
392:
388:
387:
384:
369:
366:
365:
351:
329:
325:
319:
316:
313:
310:
301:
298:
295:
291:
288:
285:
282:
279:
276:
273:
270:
267:
264:
262:
259:
258:
249:
246:
243:
240:
237:
234:
232:
228:
225:
223:
219:
215:
214:Boy's surface
212:
211:
202:
199:
197:
193:
189:
188:Roman surface
186:
184:
181:
179:
176:
173:
170:
168:
165:
164:
161:
153:
150:
148:
145:
143:
140:
138:
137:Monkey saddle
135:
133:
130:
127:
124:
122:
119:
116:
113:
112:
109:
101:
98:
96:
93:
91:
88:
86:
83:
81:
78:
76:
73:
71:
68:
67:
64:
57:
54:
53:
50:
40:
38:
34:
30:
19:
862:
849:
793:Labs surface
753:
744:
726:
671:
658:Fano surface
628:
571:
545:
459:Wave surface
411:Betti number
391:Betti number
222:affine space
196:affine space
132:Fermat cubic
26:
814:orbit space
441:K3 surfaces
85:Hyperboloid
913:Categories
889:Some more
844:References
229:, a nonic
90:Paraboloid
35:following
158:Rational
106:Rational
80:Ellipsoid
897:Pictures
827:See also
220:in real
194:in real
100:Spheroid
75:Cylinder
759:is even
648:Mumford
478:Smooth
869:
856:
292:, the
95:Sphere
867:ISBN
854:ISBN
201:Tori
646:or
915::
697::
413::
393::
39:.
757:1
754:b
745:h
600:)
530:.
516:3
511:P
352:n
330:2
326:C
320:1
317:+
314:n
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.