Volume 15, issue 3 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 29
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
The moduli space of stable quotients

Alina Marian, Dragos Oprea and Rahul Pandharipande

Geometry & Topology 15 (2011) 1651–1706
Bibliography
1 E Arbarello, M Cornalba, P A Griffiths, J Harris, Geometry of algebraic curves, Vol. I, Grundlehren der Math. Wissenschaften 267, Springer (1985) MR770932
2 K Behrend, B Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997) 45 MR1437495
3 I Ciocan-Fontanine, M Kapranov, Virtual fundamental classes via dg-manifolds, Geom. Topol. 13 (2009) 1779 MR2496057
4 I Ciocan-Fontanine, B Kim, Moduli stacks of stable toric quasimaps, Adv. Math. 225 (2010) 3022 MR2729000
5 Y Cooper, The geometry of stable quotients in genus $1$, in preparation
6 C Faber, A conjectural description of the tautological ring of the moduli space of curves, from: "Moduli of curves and abelian varieties" (editors C Faber, E Looijenga), Aspects Math. E33, Vieweg (1999) 109 MR1722541
7 C Faber, R Pandharipande, Hodge integrals and Gromov–Witten theory, Invent. Math. 139 (2000) 173 MR1728879
8 W Fulton, Intersection theory, Ergebnisse der Math. und ihrer Grenzgebiete (3) 2, Springer (1984) MR732620
9 E Getzler, R Pandharipande, The Betti numbers of $\mskip2mu\wbar{\mskip-2mu\mathscr M\mskip1mu}\mskip-1mu_{0,n}(r,d)$, J. Algebraic Geom. 15 (2006) 709 MR2237267
10 D Gillam, Deformations of quotients on a product arXiv:1103.5482
11 A B Givental, Equivariant Gromov–Witten invariants, Internat. Math. Res. Notices (1996) 613 MR1408320
12 T Graber, R Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999) 487 MR1666787
13 J Harris, I Morrison, Moduli of curves, Graduate Texts in Math. 187, Springer (1998) MR1631825
14 B Hassett, Moduli spaces of weighted pointed stable curves, Adv. Math. 173 (2003) 316 MR1957831
15 Y Hu, J Li, Genus-one stable maps, local equations, and Vakil–Zinger's desingularization, Math. Ann. 348 (2010) 929 MR2721647
16 D Joyce, Configurations in abelian categories. IV. Invariants and changing stability conditions, Adv. Math. 217 (2008) 125 MR2357325
17 B Kim, A Kresch, Y G Oh, A compactification of the space of maps from curves arXiv:1105.6143
18 B Kim, R Pandharipande, The connectedness of the moduli space of maps to homogeneous spaces, from: "Symplectic geometry and mirror symmetry (Seoul, 2000)" (editors K Fukaya, Y G Oh, K Ono, G Tian), World Sci. Publ. (2001) 187 MR1882330
19 A Klemm, R Pandharipande, Enumerative geometry of Calabi–Yau $4$–folds, Comm. Math. Phys. 281 (2008) 621 MR2415462
20 M Kontsevich, Y Soibelman, Stability structures, motivic Donaldson–Thomas invariants and cluster transformations arXiv:0811.2435
21 J Lee, T H Parker, A structure theorem for the Gromov–Witten invariants of Kähler surfaces, J. Differential Geom. 77 (2007) 483 MR2362322
22 J Li, G Tian, Virtual moduli cycles and Gromov–Witten invariants of algebraic varieties, J. Amer. Math. Soc. 11 (1998) 119 MR1467172
23 B H Lian, K Liu, S T Yau, Mirror principle. I \rm\hrefhttp://www.ams.org/mathscinet-getitem?mr=1621573[MR1621573], from: "Surveys in differential geometry V: Differential geometry inspired by string theory" (editor S T Yau), Surv. Differ. Geom. 5, Int. Press (1999) 405 MR1772275
24 E Looijenga, On the tautological ring of $\mathscr{M}_g$, Invent. Math. 121 (1995) 411 MR1346214
25 A Losev, Y Manin, New moduli spaces of pointed curves and pencils of flat connections, Michigan Math. J. 48 (2000) 443 MR1786500
26 C Manolache, Virtual push-forwards arXiv:1010.2704
27 A Marian, D Oprea, Virtual intersections on the Quot scheme and Vafa–Intriligator formulas, Duke Math. J. 136 (2007) 81 MR2271296
28 D Maulik, N Nekrasov, A Okounkov, R Pandharipande, Gromov–Witten theory and Donaldson–Thomas theory, I, Compos. Math. 142 (2006) 1263 MR2264664
29 D Maulik, N Nekrasov, A Okounkov, R Pandharipande, Gromov–Witten theory and Donaldson–Thomas theory, II, Compos. Math. 142 (2006) 1286 MR2264665
30 C Okonek, M Schneider, H Spindler, Vector bundles on complex projective spaces, Progress in Math. 3, Birkhäuser (1980) MR561910
31 R Pandharipande, The kappa ring of the moduli space of curves of compact type I arXiv:0906.2657
32 R Pandharipande, The kappa ring of the moduli space of curves of compact type II arXiv:0906:2658
33 R Pandharipande, A compactification over $\wwbar {M}_g$ of the universal moduli space of slope-semistable vector bundles, J. Amer. Math. Soc. 9 (1996) 425 MR1308406
34 R Pandharipande, Hodge integrals and degenerate contributions, Comm. Math. Phys. 208 (1999) 489 MR1729095
35 R Pandharipande, A Pixton, Relations in the tautological ring arXiv:1101.2236
36 R Pandharipande, R P Thomas, Curve counting via stable pairs in the derived category, Invent. Math. 178 (2009) 407 MR2545686
37 R Pandharipande, A Zinger, Enumerative geometry of Calabi–Yau $5$–folds, from: "New developments in algebraic geometry, integrable systems and mirror symmetry (RIMS, Kyoto, 2008)" (editors M H Saito, S Hosono, K Yoshioka), Adv. Stud. Pure Math. 59, Math. Soc. Japan (2010) 239 MR2683212
38 M Popa, M Roth, Stable maps and Quot schemes, Invent. Math. 152 (2003) 625 MR1988296
39 C H Taubes, $\mathrm{GR}=\mathrm{SW}$: counting curves and connections, J. Differential Geom. 52 (1999) 453 MR1761081
40 R P Thomas, A holomorphic Casson invariant for Calabi–Yau $3$–folds, and bundles on $K3$ fibrations, J. Differential Geom. 54 (2000) 367 MR1818182
41 J F Thomsen, Irreducibility of $\wwbar{M}_{0,n}(G/P,\beta)$, Internat. J. Math. 9 (1998) 367 MR1625369
42 Y Toda, Moduli spaces of stable quotients and the wall-crossing phenomena, to appear in Compos. Math. arXiv:1005.3743
43 R Vakil, A Zinger, A desingularization of the main component of the moduli space of genus-one stable maps into $\mathbb P^n$, Geom. Topol. 12 (2008) 1 MR2377245
44 A Zinger, The reduced genus $1$ Gromov–Witten invariants of Calabi–Yau hypersurfaces, J. Amer. Math. Soc. 22 (2009) 691 MR2505298