Geometry & Topology

Towards a quantum Lefschetz hyperplane theorem in all genera

Honglu Fan and Yuan-Pin Lee

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Abstract

An effective algorithm of determining Gromov–Witten invariants of smooth hypersurfaces in any genus (subject to a degree bound) from Gromov–Witten invariants of the ambient space is proposed.

Article information

Source
Geom. Topol., Volume 23, Number 1 (2019), 493-512.

Dates
Received: 19 December 2017
Revised: 20 April 2018
Accepted: 20 May 2018
First available in Project Euclid: 12 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.gt/1552356086

Digital Object Identifier
doi:10.2140/gt.2019.23.493

Mathematical Reviews number (MathSciNet)
MR3921324

Zentralblatt MATH identifier
07034550

Subjects
Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]

Keywords
Gromov–Witten quantum Lefschetz hyperplane theorem

Citation

Fan, Honglu; Lee, Yuan-Pin. Towards a quantum Lefschetz hyperplane theorem in all genera. Geom. Topol. 23 (2019), no. 1, 493--512. doi:10.2140/gt.2019.23.493. https://projecteuclid.org/euclid.gt/1552356086


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References

  • M Bershadsky, S Cecotti, H Ooguri, C Vafa, Holomorphic anomalies in topological field theories, Nuclear Phys. B 405 (1993) 279–304
  • 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) 311–427
  • H-L Chang, S Guo, W-P Li, J Zhou, Genus one GW invariants of quintic threefolds via MSP localization, preprint (2017)
  • 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)
  • T Coates, A Givental, Quantum Riemann–Roch, Lefschetz and Serre, Ann. of Math. 165 (2007) 15–53
  • H Fan, Y-P Lee, On Gromov–Witten theory of projective bundles, preprint (2016)
  • H Fan, Y-P Lee, Towards a quantum Lefschetz hyperplane theorem in all genera, preprint (2017)
  • A B Givental, Equivariant Gromov–Witten invariants, Internat. Math. Res. Notices 1996 (1996) 613–663
  • A B Givental, Gromov–Witten invariants and quantization of quadratic Hamiltonians, Mosc. Math. J. 1 (2001) 551–568
  • S Guo, F Janda, Y Ruan, A mirror theorem for genus two Gromov–Witten invariants of quintic threefolds, preprint (2017)
  • S Guo, D Ross, Genus-one mirror symmetry in the Landau–Ginzburg model, preprint (2016)
  • S Guo, D Ross, The genus-one global mirror theorem for the quintic threefold, preprint (2017)
  • E-N Ionel, T H Parker, The Gopakumar–Vafa formula for symplectic manifolds, Ann. of Math. 187 (2018) 1–64
  • B Kim, Quantum hyperplane section theorem for homogeneous spaces, Acta Math. 183 (1999) 71–99
  • B Kim, A Kresch, T Pantev, Functoriality in intersection theory and a conjecture of Cox, Katz, and Lee, J. Pure Appl. Algebra 179 (2003) 127–136
  • B Kim, H Lho, Mirror theorem for elliptic quasimap invariants, Geom. Topol. 22 (2018) 1459–1481
  • M Kontsevich, Enumeration of rational curves via torus actions, from “The moduli space of curves” (R Dijkgraaf, C Faber, G van der Geer, editors), Progr. Math. 129, Birkhäuser, Boston (1995) 335–368
  • Y-P Lee, Quantum Lefschetz hyperplane theorem, Invent. Math. 145 (2001) 121–149
  • Y-P Lee, R Pandharipande, A reconstruction theorem in quantum cohomology and quantum $K$–theory, Amer. J. Math. 126 (2004) 1367–1379
  • C-C M Liu, Localization in Gromov–Witten theory and orbifold Gromov–Witten theory, from “Handbook of moduli, II” (G Farkas, I Morrison, editors), Adv. Lect. Math. 25, Int., Somerville, MA (2013) 353–425
  • A Mustata, A Mustata, Gromov–Witten invariants for varieties with $C^*$ action, preprint (2015)
  • L Wu, A remark on Gromov–Witten invariants of quintic threefold, Adv. Math. 326 (2018) 241–313
  • A Zinger, The reduced genus $1$ Gromov–Witten invariants of Calabi–Yau hypersurfaces, J. Amer. Math. Soc. 22 (2009) 691–737