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40:
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477:
The study of stacky curves is used extensively in equivariant Gromov–Witten theory and enumerative geometry.
735:
600:
455:
471:
48:
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661:
524:
273:
164:
77:
44:
605:
643:
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36:
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558:
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Landesman, Aaron; Ruhm, Peter; Zhang, Robin (2016). "Spin canonical rings of log stacky curves".
514:
24:
711:
618:
267:
158:
703:
610:
599:. Proc. Sympos. Pure Math. Vol. 80. Providence, RI: Amer. Math. Soc. pp. 259–271.
568:
109:
106:
28:
699:
665:
528:
592:
459:
405:{\displaystyle d=\deg K_{\mathfrak {X}}=2-2g-\sum _{i=1}^{r}{\frac {n_{i}-1}{n_{i}}}.}
729:
595:; Bertram, Aaron; Katzarkov, Ludmil; Pandharipande, Rahul; Thaddeus, Michael (eds.).
103:
680:
638:
707:
131:
A stacky curve is uniquely determined (up to isomorphism) by its coarse space
715:
470:
The generalization of GAGA for stacky curves is used in the derivation of
55:
591:
Kresch, Andrew (2009). "On the geometry of
Deligne-Mumford stacks". In
614:
656:
641:; Noohi, Behrang (2006). "Uniformization of Deligne-Mumford curves".
572:
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519:
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does not hold for stacky curves, there is a generalization of
303:
276:
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80:
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algebraic structure theory of rings of modular forms
54:Stacky curves are closely related to 1-dimensional
404:
286:
243:
177:
90:
244:{\displaystyle K_{\mathfrak {X}}\sim K_{X}+R.}
157:(its ramification orders) greater than 1. The
462:and the category of complex orbifold curves.
8:
511:Memoirs of the American Mathematical Society
31:with potentially "fractional points" called
505:Voight, John; Zureick-Brown, David (2015).
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681:"Equivariant GW Theory of Stacky Curves"
586:
584:
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442:Although the corresponding statement of
597:Algebraic Geometry: Seattle 2005 Part 1
486:
189:to the sum of the canonical divisor of
688:Communications in Mathematical Physics
123:that contains a dense open subscheme.
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507:The canonical ring of a stacky curve
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83:
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150:(its stacky points) and integers
287:{\displaystyle {\mathfrak {X}}}
178:{\displaystyle {\mathfrak {X}}}
91:{\displaystyle {\mathfrak {X}}}
58:and therefore sometimes called
35:. A stacky curve is a type of
1:
550:Annales de l'Institut Fourier
16:Object in algebraic geometry
448:Riemann's existence theorem
193:and a ramification divisor
752:
458:of stacky curves over the
143:), a finite set of points
708:10.1007/s00220-014-2021-1
452:equivalence of categories
415:A stacky curve is called
110:geometrically connected
679:Johnson, Paul (2014).
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49:rings of modular forms
644:J. Reine Angew. Math.
407:
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113:Deligne–Mumford stack
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444:Riemann–Roch theorem
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266:, the degree of the
262:of the coarse space
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45:enumerative geometry
41:Gromov–Witten theory
700:2014CMaPh.327..333J
666:2005math......4309B
529:2015arXiv150104657V
187:linearly equivalent
27:that is roughly an
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25:algebraic geometry
19:In mathematics, a
624:978-0-8218-4702-2
615:10.5167/uzh-21342
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268:canonical divisor
159:canonical divisor
39:used in studying
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557:(6): 2339–2383.
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23:is an object in
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593:Abramovich, Dan
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460:complex numbers
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74:A stacky curve
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60:orbifold curves
29:algebraic curve
17:
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5:
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694:(2): 333–386.
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450:that gives an
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736:Moduli theory
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439:is negative.
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431:is zero, and
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98:over a field
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33:stacky points
30:
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657:math/0504309
647:
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639:Behrend, Kai
633:
596:
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466:Applications
454:between the
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21:stacky curve
20:
18:
650:: 111–153.
139:curve over
564:1507.02643
520:1501.04657
481:References
433:hyperbolic
135:(a smooth
127:Properties
70:Definition
64:orbicurves
716:1432-0916
601:CiteSeerX
425:Euclidean
417:spherical
381:−
348:∑
344:−
335:−
314:
220:∼
117:dimension
56:orbifolds
730:Category
456:category
254:Letting
696:Bibcode
662:Bibcode
525:Bibcode
258:be the
119:1 over
714:
621:
603:
107:proper
104:smooth
47:, and
684:(PDF)
652:arXiv
559:arXiv
515:arXiv
260:genus
102:is a
37:stack
712:ISSN
619:ISBN
704:doi
692:327
648:599
611:doi
569:doi
435:if
427:if
419:if
311:deg
270:of
185:is
161:of
115:of
62:or
732::
710:.
702:.
690:.
686:.
660:.
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609:.
581:^
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555:66
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537:^
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718:.
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664::
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571::
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527::
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437:d
429:d
421:d
400:.
393:i
389:n
384:1
376:i
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358:1
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352:i
341:g
338:2
332:2
329:=
323:X
318:K
308:=
305:d
280:X
264:X
256:g
239:.
236:R
233:+
228:X
224:K
214:X
209:K
195:R
191:X
171:X
154:i
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147:i
145:x
141:k
133:X
121:k
100:k
84:X
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