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

Volume 29
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
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
Higher genus FJRW invariants of a Fermat cubic

Jun Li, Yefeng Shen and Jie Zhou

Geometry & Topology 27 (2023) 1845–1890
Bibliography
1 A Basalaev, N Priddis, Givental-type reconstruction at a nonsemisimple point, Michigan Math. J. 67 (2018) 333 MR3802257
2 P Belorousski, R Pandharipande, A descendent relation in genus 2, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 29 (2000) 171 MR1765541
3 S Bloch, A Okounkov, The character of the infinite wedge representation, Adv. Math. 149 (2000) 1 MR1742353
4 H L Chang, Y H Kiem, J Li, Algebraic virtual cycles for quantum singularity theories, Comm. Anal. Geom. 29 (2021) 1749 MR4429243
5 H L Chang, J Li, An algebraic proof of the hyperplane property of the genus one GW-invariants of quintics, J. Differential Geom. 100 (2015) 251 MR3343833
6 H L Chang, J Li, W P Li, Witten’s top Chern class via cosection localization, Invent. Math. 200 (2015) 1015 MR3348143
7 H L Chang, J Li, W P Li, C C M Liu, Mixed-spin-P fields of Fermat polynomials, Camb. J. Math. 7 (2019) 319 MR4010064
8 H L Chang, J Li, W P Li, C C M Liu, An effective theory of GW and FJRW invariants of quintic Calabi–Yau manifolds, J. Differential Geom. 120 (2022) 251 MR4385118
9 A Chiodo, Towards an enumerative geometry of the moduli space of twisted curves and rth roots, Compos. Math. 144 (2008) 1461 MR2474317
10 A Chiodo, H Iritani, Y Ruan, Landau–Ginzburg/Calabi–Yau correspondence, global mirror symmetry and Orlov equivalence, Publ. Math. Inst. Hautes Études Sci. 119 (2014) 127 MR3210178
11 A Chiodo, Y Ruan, Landau–Ginzburg/Calabi–Yau correspondence for quintic three-folds via symplectic transformations, Invent. Math. 182 (2010) 117 MR2672282
12 A Chiodo, Y Ruan, A global mirror symmetry framework for the Landau–Ginzburg/Calabi–Yau correspondence, Ann. Inst. Fourier (Grenoble) 61 (2011) 2803 MR3112509
13 A Chiodo, Y Ruan, LG/CY correspondence : the state space isomorphism, Adv. Math. 227 (2011) 2157 MR2807086
14 E Clader, Landau–Ginzburg/Calabi–Yau correspondence for the complete intersections X3,3 and X2,2,2,2, Adv. Math. 307 (2017) 1 MR3590512
15 B Dubrovin, Y Zhang, Frobenius manifolds and Virasoro constraints, Selecta Math. 5 (1999) 423 MR1740678
16 T Eguchi, K Hori, C S Xiong, Quantum cohomology and Virasoro algebra, Phys. Lett. B 402 (1997) 71 MR1454328
17 C Faber, R Pandharipande, Relative maps and tautological classes, J. Eur. Math. Soc. 7 (2005) 13 MR2120989
18 C Faber, S Shadrin, D Zvonkine, Tautological relations and the r–spin Witten conjecture, Ann. Sci. Éc. Norm. Supér. 43 (2010) 621 MR2722511
19 H Fan, T J Jarvis, Y Ruan, The Witten equation and its virtual fundamental cycle, preprint (2007) arXiv:0712.4025
20 H Fan, T Jarvis, Y Ruan, The Witten equation, mirror symmetry, and quantum singularity theory, Ann. of Math. 178 (2013) 1 MR3043578
21 A Francis, Computational techniques in FJRW theory with applications to Landau–Ginzburg mirror symmetry, Adv. Theor. Math. Phys. 19 (2015) 1339 MR3501062
22 A B Givental, Gromov–Witten invariants and quantization of quadratic Hamiltonians, Mosc. Math. J. 1 (2001) 551 MR1901075
23 A B Givental, Semisimple Frobenius structures at higher genus, Int. Math. Res. Not. (2001) 1265 MR1866444
24 B R Greene, C Vafa, N P Warner, Calabi–Yau manifolds and renormalization group flows, Nuclear Phys. B 324 (1989) 371 MR1025421
25 S Guo, D Ross, The genus-one global mirror theorem for the quintic 3–fold, Compos. Math. 155 (2019) 995 MR3946282
26 S Guo, D Ross, Genus-one mirror symmetry in the Landau–Ginzburg model, Algebr. Geom. 6 (2019) 260 MR3938619
27 W He, Y Shen, Virasoro constraints in quantum singularity theories, preprint (2021) arXiv:2103.00313
28 E N Ionel, Topological recursive relations in H2g(g,n), Invent. Math. 148 (2002) 627 MR1908062
29 H Iritani, T Milanov, Y Ruan, Y Shen, Gromov–Witten theory of quotients of Fermat Calabi–Yau varieties, 1310, Amer. Math. Soc. (2021) MR4223045
30 M Kaneko, D Zagier, A generalized Jacobi theta function and quasimodular forms, from: "The moduli space of curves" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 165 MR1363056
31 Y H Kiem, J Li, Quantum singularity theory via cosection localization, J. Reine Angew. Math. 766 (2020) 73 MR4145203
32 M Kontsevich, Y Manin, Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994) 525 MR1291244
33 M Kontsevich, Y Manin, Relations between the correlators of the topological sigma-model coupled to gravity, Comm. Math. Phys. 196 (1998) 385 MR1645019
34 M Krawitz, Y Shen, Landau–Ginzburg/Calabi–Yau correspondence of all genera for elliptic orbifold 1, preprint (2011) arXiv:1106.6270
35 Y P Lee, Notes on axiomatic Gromov–Witten theory and applications, from: "Algebraic geometry" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 309 MR2483940
36 Y P Lee, N Priddis, M Shoemaker, A proof of the Landau–Ginzburg/Calabi–Yau correspondence via the crepant transformation conjecture, Ann. Sci. Éc. Norm. Supér. 49 (2016) 1403 MR3592361
37 Y P Lee, M Shoemaker, A mirror theorem for the mirror quintic, Geom. Topol. 18 (2014) 1437 MR3228456
38 J Li, W P Li, Y Shen, J Zhou, A genus-one FJRW invariant via two methods, Math. Z. 302 (2022) 1927 MR4509017
39 E J Martinec, Criticality, catastrophes, and compactifications, from: "Physics and mathematics of strings" (editors L Brink, D Friedan, A M Polyakov), World Sci. (1990) 389 MR1104265
40 T Milanov, Y Ruan, Gromov–Witten theory of elliptic orbifold 1 and quasi-modular forms, preprint (2011) arXiv:1106.2321
41 T Milanov, Y Shen, Global mirror symmetry for invertible simple elliptic singularities, Ann. Inst. Fourier (Grenoble) 66 (2016) 271 MR3477877
42 G Oberdieck, A Pixton, Holomorphic anomaly equations and the Igusa cusp form conjecture, Invent. Math. 213 (2018) 507 MR3827207
43 A Okounkov, R Pandharipande, Gromov–Witten theory, Hurwitz theory, and completed cycles, Ann. of Math. 163 (2006) 517 MR2199225
44 A Okounkov, R Pandharipande, Virasoro constraints for target curves, Invent. Math. 163 (2006) 47 MR2208418
45 A Pixton, The Gromov–Witten theory of an elliptic curve and quasimodular forms, senior thesis, Princeton University (2008)
46 A Polishchuk, A Vaintrob, Matrix factorizations and cohomological field theories, J. Reine Angew. Math. 714 (2016) 1 MR3491884
47 A Popa, The genus one Gromov–Witten invariants of Calabi–Yau complete intersections, Trans. Amer. Math. Soc. 365 (2013) 1149 MR3003261
48 Y Ruan, The Witten equation and the geometry of the Landau–Ginzburg model, from: "String-Math 2011" (editors J Block, J Distler, R Donagi, E Sharpe), Proc. Sympos. Pure Math. 85, Amer. Math. Soc. (2012) 209 MR2985332
49 Y Shen, J Zhou, Ramanujan identities and quasi-modularity in Gromov–Witten theory, Commun. Number Theory Phys. 11 (2017) 405 MR3690254
50 Y Shen, J Zhou, LG/CY correspondence for elliptic orbifold curves via modularity, J. Differential Geom. 109 (2018) 291 MR3807321
51 J H Silverman, The arithmetic of elliptic curves, 106, Springer (2009) MR2514094
52 C Teleman, The structure of 2D semi-simple field theories, Invent. Math. 188 (2012) 525 MR2917177
53 E Urban, Nearly overconvergent modular forms, from: "Iwasawa theory 2012" (editors T Bouganis, O Venjakob), Contrib. Math. Comput. Sci. 7, Springer (2014) 401 MR3586822
54 C Vafa, N Warner, Catastrophes and the classification of conformal theories, Phys. Lett. B 218 (1989) 51 MR983349
55 K Weierstrass, Zur Theorie der elliptischen Funktionen, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin (1882) 443
56 E Witten, Phases of N = 2 theories in two dimensions, Nuclear Phys. B 403 (1993) 159 MR1232617
57 D Zagier, Elliptic modular forms and their applications, from: "The 1-2-3 of modular forms" (editor K Ranestad), Springer (2008) 1 MR2409678
58 A Zinger, The reduced genus 1 Gromov–Witten invariants of Calabi–Yau hypersurfaces, J. Amer. Math. Soc. 22 (2009) 691 MR2505298