Volume 20, issue 4 (2016)

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

Volume 26
Issue 8, 3307–3833
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

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 Interests
Editorial Procedure
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
Gromov–Witten theory of Fano orbifold curves, Gamma integral structures and ADE-Toda hierarchies

Todor Milanov, Yefeng Shen and Hsian-Hua Tseng

Geometry & Topology 20 (2016) 2135–2218
1 D Abramovich, T Graber, A Vistoli, Gromov–Witten theory of Deligne–Mumford stacks, Amer. J. Math. 130 (2008) 1337 MR2450211
2 N A’Campo, Le groupe de monodromie du déploiement des singularités isolées de courbes planes, I, Math. Ann. 213 (1975) 1 MR0377108
3 N A’Campo, Le groupe de monodromie du déploiement des singularités isolées de courbes planes, II, from: "Proceedings of the International Congress of Mathematicians", Canad. Math. Congress (1975) 395 MR0435443
4 V I Arnol’d, S M Guseĭn-Zade, A N Varchenko, Singularities of differentiable maps, II : Monodromy and asymptotics of integrals, 83, Birkhäuser (1988) MR966191
5 B Bakalov, T Milanov, 𝒲–constraints for the total descendant potential of a simple singularity, Compos. Math. 149 (2013) 840 MR3069364
6 A Buryak, H Posthuma, S Shadrin, On deformations of quasi-Miura transformations and the Dubrovin–Zhang bracket, J. Geom. Phys. 62 (2012) 1639 MR2922026
7 A Buryak, H Posthuma, S Shadrin, A polynomial bracket for the Dubrovin–Zhang hierarchies, J. Differential Geom. 92 (2012) 153 MR2998900
8 C Cadman, Using stacks to impose tangency conditions on curves, Amer. J. Math. 129 (2007) 405 MR2306040
9 G Carlet, The extended bigraded Toda hierarchy, J. Phys. A 39 (2006) 9411 MR2246697
10 G Carlet, B Dubrovin, Y Zhang, The extended Toda hierarchy, Mosc. Math. J. 4 (2004) 313 MR2108440
11 W Chen, Y Ruan, Orbifold Gromov–Witten theory, from: "Orbifolds in mathematics and physics" (editors A Adem, J Morava, Y Ruan), Contemp. Math. 310, Amer. Math. Soc. (2002) 25 MR1950941
12 T Coates, A Corti, H Iritani, H H Tseng, Computing genus-zero twisted Gromov–Witten invariants, Duke Math. J. 147 (2009) 377 MR2510741
13 T Coates, A Corti, H Iritani, H H Tseng, A mirror theorem for toric stacks, Compos. Math. 151 (2015) 1878 MR3414388
14 E Date, M Jimbo, M Kashiwara, T Miwa, Transformation groups for soliton equations, III : Operator approach to the Kadomtsev–Petviashvili equation, J. Phys. Soc. Japan 50 (1981) 3806 MR638807
15 B Dubrovin, Geometry of 2D topological field theories, from: "Integrable systems and quantum groups" (editors M Francaviglia, S Greco), Lecture Notes in Math. 1620, Springer (1996) 120 MR1397274
16 B Dubrovin, Y Zhang, Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov–Witten invariants, (2001) arXiv:math/0108160v1
17 E Frenkel, A Givental, T Milanov, Soliton equations, vertex operators, and simple singularities, Funct. Anal. Other Math. 3 (2010) 47 MR2734560
18 I B Frenkel, V G Kac, Basic representations of affine Lie algebras and dual resonance models, Invent. Math. 62 (1980/81) 23 MR595581
19 S Galkin, V Golyshev, H Iritani, Gamma classes and quantum cohomology of Fano manifolds : Gamma conjectures, Duke Math. J. 165 (2016) 2005 MR3536989
20 A Givental, A mirror theorem for toric complete intersections, from: "Topological field theory, primitive forms and related topics" (editors M Kashiwara, A Matsuo, K Saito, I Satake), Progr. Math. 160, Birkhäuser (1998) 141 MR1653024
21 A B Givental, Gromov–Witten invariants and quantization of quadratic Hamiltonians, Mosc. Math. J. 1 (2001) 551 MR1901075
22 A B Givental, Semisimple Frobenius structures at higher genus, Internat. Math. Res. Notices (2001) 1265 MR1866444
23 A Givental, An1 singularities and nKdV hierarchies, Mosc. Math. J. 3 (2003) 475 MR2025270
24 A B Givental, T E Milanov, Simple singularities and integrable hierarchies, from: "The breadth of symplectic and Poisson geometry" (editors J E Marsden, T S Ratiu), Progr. Math. 232, Birkhäuser (2005) 173 MR2103007
25 P A Griffiths, On the periods of certain rational integrals, I, Ann. of Math. 90 (1969) 460 MR0260733
26 P A Griffiths, On the periods of certain rational integrals, II, Ann. of Math. 90 (1969) 496 MR0260733
27 S M Guseĭn-Zade, Dynkin diagrams of the singularities of functions of two variables, Funkcional. Anal. i Priložen. 8 (1974) 23 MR0430302
28 S M Guseĭn-Zade, Intersection matrices for certain singularities of functions of two variables, Funkcional. Anal. i Priložen. 8 (1974) 11 MR0338437
29 C Hertling, Frobenius manifolds and moduli spaces for singularities, 151, Cambridge Univ. Press (2002) MR1924259
30 H Iritani, An integral structure in quantum cohomology and mirror symmetry for toric orbifolds, Adv. Math. 222 (2009) 1016 MR2553377
31 H Iritani, Quantum cohomology and periods, Ann. Inst. Fourier (Grenoble) 61 (2011) 2909 MR3112512
32 Y Ishibashi, Y Shiraishi, A Takahashi, Primitive forms for affine cusp polynomials, preprint (2012) arXiv:1211.1128
33 V G Kac, Infinite-dimensional Lie algebras, Cambridge Univ. Press (1990) MR1104219
34 V Kac, Vertex algebras for beginners, 10, Amer. Math. Soc. (1998) MR1651389
35 V G Kac, D H Peterson, 112 constructions of the basic representation of the loop group of E8, from: "Symposium on anomalies, geometry, topology" (editors W A Bardeen, A R White), World Sci. (1985) 276 MR850863
36 V G Kac, M Wakimoto, Exceptional hierarchies of soliton equations, from: "Theta functions" (editors L Ehrenpreis, R C Gunning), Proc. Sympos. Pure Math. 49, Amer. Math. Soc. (1989) 191 MR1013133
37 L Katzarkov, M Kontsevich, T Pantev, Hodge theoretic aspects of mirror symmetry, from: "From Hodge theory to integrability and TQFT tt*–geometry" (editors R Y Donagi, K Wendland), Proc. Sympos. Pure Math. 78, Amer. Math. Soc. (2008) 87 MR2483750
38 M Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 (1992) 1 MR1171758
39 T E Milanov, Hirota quadratic equations for the extended Toda hierarchy, Duke Math. J. 138 (2007) 161 MR2309158
40 T E Milanov, H H Tseng, The spaces of Laurent polynomials, Gromov–Witten theory of 1–orbifolds, and integrable hierarchies, J. Reine Angew. Math. 622 (2008) 189 MR2433616
41 P Rossi, Gromov–Witten theory of orbicurves, the space of tri-polynomials and symplectic field theory of Seifert fibrations, Math. Ann. 348 (2010) 265 MR2672302
42 A N Rudakov, Markov numbers and exceptional bundles on P2, Izv. Akad. Nauk SSSR Ser. Mat. 52 (1988) 100, 240 MR936525
43 K Saito, On the periods of primitive integrals, I, (1982)
44 K Saito, A Takahashi, From primitive forms to Frobenius manifolds, from: "From Hodge theory to integrability and TQFT tt*-geometry" (editors R Y Donagi, K Wendland), Proc. Sympos. Pure Math. 78, Amer. Math. Soc. (2008) 31 MR2483747
45 M Sato, Soliton equations as dynamical systems on infinite-dimensional Grassmann manifold, from: "Random systems and dynamical systems", RIMS Kokyuroku 439, Res. Inst. Math. Sci. Kyoto Univ. (1981) 30
46 R Steinberg, Finite subgroups of SU2, Dynkin diagrams and affine Coxeter elements, Pacific J. Math. 118 (1985) 587 MR789195
47 R Stekolshchik, Notes on Coxeter transformations and the McKay correspondence, Springer (2008) MR2388772
48 A Takahashi, Mirror symmetry between orbifold projective lines and cusp singularities, from: "Singularities in geometry and topology" (editors V Blanlœil, O Saeki), Adv. Stud. Pure Math. 66, Math. Soc. Japan (2015) 257 MR3382052
49 C Teleman, The structure of 2D semi-simple field theories, Invent. Math. 188 (2012) 525 MR2917177
50 H H Tseng, Orbifold quantum Riemann–Roch, Lefschetz and Serre, Geom. Topol. 14 (2010) 1 MR2578300
51 E Witten, Two-dimensional gravity and intersection theory on moduli space, from: "Surveys in differential geometry", Lehigh Univ. (1991) 243 MR1144529