Geometry & Topology Volume 23, issue 1 (2019)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Towards a quantum Lefschetz hyperplane theorem in all genera

Honglu Fan and Yuan-Pin Lee

Geometry & Topology 23 (2019) 493–512

DOI: 10.2140/gt.2019.23.493

Bibliography

1	M Bershadsky, S Cecotti, H Ooguri, C Vafa, Holomorphic anomalies in topological field theories, Nuclear Phys. B 405 (1993) 279 MR1240687
2	M Bershadsky, S Cecotti, H Ooguri, C Vafa, Kodaira–Spencer theory of gravity and exact results for quantum string amplitudes, Comm. Math. Phys. 165 (1994) 311 MR1301851
3	H L Chang, S Guo, W P Li, J Zhou, Genus one GW invariants of quintic threefolds via MSP localization, preprint (2017) arXiv:1711.10118
4	H L Chang, J Li, W P Li, C C M Liu, An effective theory of GW and FJRW invariants of quintics Calabi–Yau manifolds, preprint (2016) arXiv:1603.06184
5	T Coates, A Givental, Quantum Riemann–Roch, Lefschetz and Serre, Ann. of Math. 165 (2007) 15 MR2276766
6	H Fan, Y P Lee, On Gromov–Witten theory of projective bundles, preprint (2016) arXiv:1607.00740
7	H Fan, Y P Lee, Towards a quantum Lefschetz hyperplane theorem in all genera, preprint (2017) arXiv:1712.03573
8	A B Givental, Equivariant Gromov–Witten invariants, Internat. Math. Res. Notices 1996 (1996) 613 MR1408320
9	A B Givental, Gromov–Witten invariants and quantization of quadratic Hamiltonians, Mosc. Math. J. 1 (2001) 551 MR1901075
10	S Guo, F Janda, Y Ruan, A mirror theorem for genus two Gromov–Witten invariants of quintic threefolds, preprint (2017) arXiv:1709.07392
11	S Guo, D Ross, Genus-one mirror symmetry in the Landau–Ginzburg model, preprint (2016) arXiv:1611.08876
12	S Guo, D Ross, The genus-one global mirror theorem for the quintic threefold, preprint (2017) arXiv:1703.06955
13	E N Ionel, T H Parker, The Gopakumar–Vafa formula for symplectic manifolds, Ann. of Math. 187 (2018) 1 MR3739228
14	B Kim, Quantum hyperplane section theorem for homogeneous spaces, Acta Math. 183 (1999) 71 MR1719555
15	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
16	B Kim, H Lho, Mirror theorem for elliptic quasimap invariants, Geom. Topol. 22 (2018) 1459 MR3780438
17	M Kontsevich, Enumeration of rational curves via torus actions, from: "The moduli space of curves" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 335 MR1363062
18	Y P Lee, Quantum Lefschetz hyperplane theorem, Invent. Math. 145 (2001) 121 MR1839288
19	Y P Lee, R Pandharipande, A reconstruction theorem in quantum cohomology and quantum K–theory, Amer. J. Math. 126 (2004) 1367 MR2102400
20	C C M Liu, Localization in Gromov–Witten theory and orbifold Gromov–Witten theory, from: "Handbook of moduli, II" (editors G Farkas, I Morrison), Adv. Lect. Math. 25, Int. (2013) 353 MR3184181
21	A Mustata, A Mustata, Gromov–Witten invariants for varieties with C^∗ action, preprint (2015) arXiv:1505.01471
22	L Wu, A remark on Gromov–Witten invariants of quintic threefold, Adv. Math. 326 (2018) 241 MR3758430
23	A Zinger, The reduced genus 1 Gromov–Witten invariants of Calabi–Yau hypersurfaces, J. Amer. Math. Soc. 22 (2009) 691 MR2505298