Volume 14, issue 1 (2010)

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

Volume 29, 1 issue

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
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Orbifold quantum Riemann–Roch, Lefschetz and Serre

Hsian-Hua Tseng

Geometry & Topology 14 (2010) 1–81
Bibliography
1 D Abramovich, T Graber, M Olsson, H H Tseng, On the global quotient structure of the space of twisted stable maps to a quotient stack, J. Algebraic Geom. 16 (2007) 731 MR2357688
2 D Abramovich, T Graber, A Vistoli, Algebraic orbifold quantum products, from: "Orbifolds in mathematics and physics (Madison, WI, 2001)" (editors A Adem, J Morava, Y Ruan), Contemp. Math. 310, Amer. Math. Soc. (2002) 1 MR1950940
3 D Abramovich, T Graber, A Vistoli, Gromov–Witten theory of Deligne–Mumford stacks, Amer. J. Math. 130 (2008) 1337 MR2450211
4 D Abramovich, A Vistoli, Compactifying the space of stable maps, J. Amer. Math. Soc. 15 (2002) 27 MR1862797
5 K Behrend, Gromov–Witten invariants in algebraic geometry, Invent. Math. 127 (1997) 601 MR1431140
6 K Behrend, Cohomology of stacks, from: "Intersection theory and moduli" (editors E Arbarello, G Ellingsrud, L Goettsche), ICTP Lect. Notes XIX, Abdus Salam Int. Cent. Theoret. Phys. (2004) 249 MR2172499
7 K Behrend, D Edidin, B Fantechi, W Fulton, L Göttsche, A Kresch, Introduction to stacks, Book in preparation
8 K Behrend, B Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997) 45 MR1437495
9 K Behrend, G Ginot, B Noohi, P Xu, String topology for stacks arXiv:0712.3857
10 K Behrend, Y Manin, Stacks of stable maps and Gromov–Witten invariants, Duke Math. J. 85 (1996) 1 MR1412436
11 A Bertram, Another way to enumerate rational curves with torus actions, Invent. Math. 142 (2000) 487 MR1804158
12 L A Borisov, L Chen, G G Smith, The orbifold Chow ring of toric Deligne–Mumford stacks, J. Amer. Math. Soc. 18 (2005) 193 MR2114820
13 J Bryan, T Graber, R Pandharipande, The orbifold quantum cohomology of $\C^2/Z_3$ and Hurwitz–Hodge integrals, J. Algebraic Geom. 17 (2008) 1 MR2357679
14 C Cadman, Quantum cohomology of stacks and enumerative applications, PhD thesis, Columbia University (2004)
15 W Chen, Y Ruan, Orbifold Gromov–Witten theory, from: "Orbifolds in mathematics and physics (Madison, WI, 2001)" (editors A Adem, J Morava, Y Ruan), Contemp. Math. 310, Amer. Math. Soc. (2002) 25 MR1950941
16 W Chen, Y Ruan, A new cohomology theory of orbifold, Comm. Math. Phys. 248 (2004) 1 MR2104605
17 T Coates, Riemann–Roch theorems in Gromov–Witten theory, PhD thesis, University of California Berkeley (2003)
18 T Coates, A Corti, H Iritani, H H Tseng, Computing genus-zero twisted Gromov–Witten invariants, Duke Math. J. 147 (2009) 377 MR2510741
19 T Coates, A Givental, Quantum Riemann–Roch, Lefschetz and Serre, Ann. of Math. $(2)$ 165 (2007) 15 MR2276766
20 T Coates, H Iritani, H H Tseng, Wall-crossings in toric Gromov–Witten theory I: Crepant examples, Geom. Topol. 13 (2009) 2675
21 T Coates, Y P Lee, A Corti, H H Tseng, The quantum orbifold cohomology of weighted projective spaces, Acta Math. 202 (2009) 139 MR2506749
22 D A Cox, S Katz, Mirror symmetry and algebraic geometry, Math. Surveys and Monogr. 68, Amer. Math. Soc. (1999) MR1677117
23 D Edidin, Notes on the construction of the moduli space of curves, from: "Recent progress in intersection theory (Bologna, 1997)" (editors G Ellingsrud, W Fulton, A Vistoli), Trends Math., Birkhäuser (2000) 85 MR1849292
24 D Edidin, B Hassett, A Kresch, A Vistoli, Brauer groups and quotient stacks, Amer. J. Math. 123 (2001) 761 MR1844577
25 C Faber, R Pandharipande, Hodge integrals and Gromov–Witten theory, Invent. Math. 139 (2000) 173 MR1728879
26 B Fantechi, Stacks for everybody, from: "European Congress of Mathematics, Vol. I (Barcelona, 2000)", Progr. Math. 201, Birkhäuser (2001) 349 MR1905329
27 W Fulton, Intersection theory, Ergebnisse der Math. und ihrer Grenzgebiete (3) 2, Springer (1984) MR732620
28 A Gathmann, Relative Gromov–Witten invariants and the mirror formula, Math. Ann. 325 (2003) 393 MR1962055
29 A Givental, Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture, from: "Topics in singularity theory" (editors A Khovanskii, A Varchenko, V Vassiliev), Amer. Math. Soc. Transl. Ser. 2 180, Amer. Math. Soc. (1997) 103 MR1767115
30 A Givental, Elliptic Gromov–Witten invariants and the generalized mirror conjecture, from: "Integrable systems and algebraic geometry (Kobe/Kyoto, 1997)" (editors M H Saito, Y Shimuzu, K Ueno), World Sci. Publ. (1998) 107 MR1672116
31 A Givental, A mirror theorem for toric complete intersections, from: "Topological field theory, primitive forms and related topics (Kyoto, 1996)" (editors M Kashiwara, A Matsuo, K Saito, I Satake), Progr. Math. 160, Birkhäuser (1998) 141 MR1653024
32 A B Givental, Gromov–Witten invariants and quantization of quadratic Hamiltonians, Mosc. Math. J. 1 (2001) 551, 645 MR1901075
33 A B Givental, Symplectic geometry of Frobenius structures, from: "Frobenius manifolds" (editors C Hertling, M Marcolli), Aspects Math. E36, Vieweg (2004) 91 MR2115767
34 T J Jarvis, T Kimura, Orbifold quantum cohomology of the classifying space of a finite group, from: "Orbifolds in mathematics and physics (Madison, WI, 2001)" (editors A Adem, J Morava, Y Ruan), Contemp. Math. 310, Amer. Math. Soc. (2002) 123 MR1950944
35 A J de Jong, A result of Gabber, Preprint
36 T Kawasaki, The Riemann–Roch theorem for complex $V$–manifolds, Osaka J. Math. 16 (1979) 151 MR527023
37 S Keel, S Mori, Quotients by groupoids, Ann. of Math. $(2)$ 145 (1997) 193 MR1432041
38 B Kim, Quantum hyperplane section theorem for homogeneous spaces, Acta Math. 183 (1999) 71 MR1719555
39 B Kim, A Kresch, T Pantev, Functoriality in intersection theory and a conjecture of Cox, Katz, and Lee, J. Pure Appl. Algebra 179 (2003) 127 MR1958379
40 M Kontsevich, Enumeration of rational curves via torus actions, from: "The moduli space of curves (Texel Island, 1994)" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 335 MR1363062
41 A Kresch, Cycle groups for Artin stacks, Invent. Math. 138 (1999) 495 MR1719823
42 A Kresch, On the geometry of Deligne–Mumford stacks, from: "Algebraic geometry—Seattle 2005. Part 1" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 259 MR2483938
43 A Kresch, A Vistoli, On coverings of Deligne–Mumford stacks and surjectivity of the Brauer map, Bull. London Math. Soc. 36 (2004) 188 MR2026412
44 G Laumon, L Moret-Bailly, Champs algébriques, Ergebnisse der Math. und ihrer Grenzgebiete (3) 39, Springer (2000) MR1771927
45 Y P Lee, Quantum Lefschetz hyperplane theorem, Invent. Math. 145 (2001) 121 MR1839288
46 B H Lian, K Liu, S T Yau, Mirror principle. I, II, III, Asian J. Math. 1, 3, 3 (1997, 1999, 1999) 729, 109, 771 MR1621573
47 Y I Manin, Frobenius manifolds, quantum cohomology, and moduli spaces, Amer. Math. Soc. Colloq. Publ. 47, Amer. Math. Soc. (1999) MR1702284
48 D Mumford, Towards an enumerative geometry of the moduli space of curves, from: "Arithmetic and geometry, Vol. II" (editors M Artin, J Tate), Progr. Math. 36, Birkhäuser (1983) 271 MR717614
49 B Toen, $K$–theory and cohomology of algebraic stacks: Riemann–Roch theorems, D–modules and GAGA theorems arXiv:math.AG/9908097
50 B Toen, Théorèmes de Riemann–Roch pour les champs de Deligne–Mumford, $K$–Theory 18 (1999) 33 MR1710187
51 B Totaro, The resolution property for schemes and stacks, J. Reine Angew. Math. 577 (2004) 1 MR2108211
52 A Vistoli, Intersection theory on algebraic stacks and on their moduli spaces, Invent. Math. 97 (1989) 613 MR1005008
53 E T Whittaker, G N Watson, A course of modern analysis. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions, Cambridge Math. Library, Cambridge Univ. Press (1996) MR1424469
54 J Zhou, Crepant resolution conjecture in all genera for type A singularities arXiv:0811.2023
55 J Zhou, On computations of Hurwitz–Hodge integrals arXiv:0710.1679