Geometry & Topology Volume 13, issue 5 (2009)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Wall-crossings in toric {G}romov–{W}itten theory {I}: crepant examples

Tom Coates, Hiroshi Iritani and Hsian-Hua Tseng

Geometry & Topology 13 (2009) 2675–2744

DOI: 10.2140/gt.2009.13.2675

Bibliography

1	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
2	D Abramovich, T Graber, A Vistoli, Gromov–Witten theory of Deligne–Mumford stacks, Amer. J. Math. 130 (2008) 1337 MR2450211
3	M Aganagic, V Bouchard, A Klemm, Topological strings and (almost) modular forms, Comm. Math. Phys. 277 (2008) 771 MR2365453
4	M Audin, Torus actions on symplectic manifolds, Progress in Math. 93, Birkhäuser Verlag (2004) MR2091310
5	S Barannikov, Semi-infinite Hodge structures and mirror symmetry for projective spaces arXiv:math.AG/0010157
6	S Barannikov, Quantum periods. I. Semi-infinite variations of Hodge structures, Internat. Math. Res. Notices (2001) 1243 MR1866443
7	L A Borisov, R P Horja, Mellin–Barnes integrals as Fourier–Mukai transforms, Adv. Math. 207 (2006) 876 MR2271990
8	J Bryan, T Graber, The crepant resolution conjecture, 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) 23 MR2483931
9	P Candelas, X C de la Ossa, P S Green, L Parkes, A pair of Calabi–Yau manifolds as an exactly soluble superconformal theory, Nuclear Phys. B 359 (1991) 21 MR1115626
10	S Cecotti, C Vafa, On classification of $N=2$ supersymmetric theories, Comm. Math. Phys. 158 (1993) 569 MR1255428
11	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
12	W Chen, Y Ruan, A new cohomology theory of orbifold, Comm. Math. Phys. 248 (2004) 1 MR2104605
13	T Coates, On the crepant resolution conjecture in the local case, Comm. Math. Phys. 287 (2009) 1071 MR2486673
14	T Coates, A Corti, H Iritani, H H Tseng, Computing genus-zero twisted Gromov–Witten invariants, Duke Math. J. 147 (2009) 377 MR2510741
15	T Coates, A Corti, Y P Lee, H H Tseng, The quantum orbifold cohomology of weighted projective spaces, Acta Math. 202 (2009) 139
16	T Coates, A B Givental, Quantum Riemann–Roch, Lefschetz and Serre, Ann. of Math. $(2)$ 165 (2007) 15 MR2276766
17	T Coates, Y Ruan, Quantum cohomology and crepant resolutions: A conjecture arXiv:0710.5901v3
18	D A Cox, S Katz, Mirror symmetry and algebraic geometry, Math. Surveys and Monogr. 68, Amer. Math. Soc. (1999) MR1677117
19	A Douai, C Sabbah, Gauss–Manin systems, Brieskorn lattices and Frobenius structures. I, from: "Proceedings of the International Conference in Honor of Frédéric Pham (Nice, 2002)", Ann. Inst. Fourier (Grenoble) 53 (2003) 1055 MR2033510
20	B Dubrovin, Geometry and integrability of topological-antitopological fusion, Comm. Math. Phys. 152 (1993) 539 MR1213301
21	B Dubrovin, Geometry of $2$D topological field theories, from: "Integrable systems and quantum groups (Montecatini Terme, 1993)" (editors M Francaviglia, S Greco), Lecture Notes in Math. 1620, Springer (1996) 120 MR1397274
22	J Fernandez, Hodge structures for orbifold cohomology, Proc. Amer. Math. Soc. 134 (2006) 2511 MR2213728
23	W Fulton, R Pandharipande, Notes on stable maps and quantum cohomology, from: "Algebraic geometry—Santa Cruz 1995" (editors J Kollár, R Lazarsfeld, D R Morrison), Proc. Sympos. Pure Math. 62, Amer. Math. Soc. (1997) 45 MR1492534
24	A B Givental, Homological geometry and mirror symmetry, from: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994)", Birkhäuser (1995) 472 MR1403947
25	A B Givental, Homological geometry. I. Projective hypersurfaces, Selecta Math. $($N.S.$)$ 1 (1995) 325 MR1354600
26	A B 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
27	A B Givental, Gromov–Witten invariants and quantization of quadratic Hamiltonians, Mosc. Math. J. 1 (2001) 551, 645 MR1901075
28	A B Givental, Symplectic geometry of Frobenius structures, from: "Frobenius manifolds" (editors C Hertling, M Marcolli), Aspects Math. E36, Vieweg (2004) 91 MR2115767
29	M A Guest, Quantum cohomology via $D$–modules, Topology 44 (2005) 263 MR2114708
30	C Hertling, $tt^{}$ geometry, Frobenius manifolds, their connections, and the construction for singularities*, J. Reine Angew. Math. 555 (2003) 77 MR1956595
31	C Hertling, Y Manin, Weak Frobenius manifolds, Internat. Math. Res. Notices (1999) 277 MR1680372
32	C Hertling, Y Manin, Unfoldings of meromorphic connections and a construction of Frobenius manifolds, from: "Frobenius manifolds" (editors C Hertling, M Marcolli), Aspects Math. E36, Vieweg (2004) 113 MR2115768
33	K Hori, S Katz, A Klemm, R Pandharipande, R Thomas, C Vafa, R Vakil, E Zaslow, Mirror symmetry, Clay Math. Monogr. 1, Amer. Math. Soc. (2003) MR2003030
34	K Hori, C Vafa, Mirror symmetry arXiv:hep-th/0002222
35	P R Horja, Hypergeometric functions and mirror symmetry in toric varieties arXiv:math.AG/9912109
36	H Iritani, An integral structure in quantum cohomology and mirror symmetry for toric orbifolds, to appear in Adv. Math
37	H Iritani, Ruan's conjecture and integral structures in quantum cohomology arXiv:0809.2749
38	H Iritani, Wall-crossings in toric Gromov–Witten theory III, in preparation
39	H Iritani, Quantum $D$–modules and generalized mirror transformations, Topology 47 (2008) 225 MR2416770
40	M Kontsevich, Y Manin, Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994) 525 MR1291244
41	B H Lian, K Liu, S T Yau, Mirror principle. II, Asian J. Math. 3 (1999) 109 MR1701925
42	E Lupercio, M Poddar, The global McKay–Ruan correspondence via motivic integration, Bull. London Math. Soc. 36 (2004) 509 MR2069013
43	Y I Manin, Frobenius manifolds, quantum cohomology, and moduli spaces, Amer. Math. Soc. Coll. Publ. 47, Amer. Math. Soc. (1999) MR1702284
44	A Pressley, G Segal, Loop groups, Oxford Math. Monogr., Oxford Science Publ., The Clarendon Press, Oxford Univ. Press (1986) MR900587
45	M A Rose, A reconstruction theorem for genus zero Gromov–Witten invariants of stacks, Amer. J. Math. 130 (2008) 1427 MR2450213
46	Y Ruan, private communication
47	K Saito, Period mapping associated to a primitive form, Publ. Res. Inst. Math. Sci. 19 (1983) 1231 MR723468
48	M Saito, On the structure of Brieskorn lattice, Ann. Inst. Fourier (Grenoble) 39 (1989) 27 MR1011977
49	W Schmid, Variation of Hodge structure: the singularities of the period mapping, Invent. Math. 22 (1973) 211 MR0382272
50	E Witten arXiv:hep-th/9306122
51	T Yasuda, Twisted jets, motivic measures and orbifold cohomology, Compos. Math. 140 (2004) 396 MR2027195