Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SYMMETRY OF THE TWISTED GROMOV-WITTEN CLASSES OF PROJECTIVE LINE

  • Hyenho Lho (Department of Mathematics Chungnam National University)
  • Received : 2021.07.20
  • Accepted : 2023.01.26
  • Published : 2023.05.01
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Abstract

We study the rationality and symmetry of the Gromov-Witten invariants of the projective line twisted by certain line bundles.

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References

  1. Y. Bae, Tautological relations for stable maps to a target variety, Ark. Mat. 58 (2020), no. 1, 19-38. https://doi.org/10.4310/arkiv.2020.v58.n1.a2
  2. T. Bullese and M. Moreira, in preparation.
  3. I. Ciocan-Fontanine and B. Kim, Higher genus quasimap wall-crossing for semipositive targets, J. Eur. Math. Soc. (JEMS) 19 (2017), no. 7, 2051-2102. https://doi.org/10.4171/JEMS/713
  4. T. Coates, A. Corti, H. Iritani, and H. Tseng, Hodge-theoretic mirror symmetry for toric stacks, J. Differential Geom. 114 (2020), no. 1, 41-115. https://doi.org/10.4310/jdg/1577502022
  5. C. F. Faber and R. V. Pandharipande, Hodge integrals and Gromov-Witten theory, Invent. Math. 139 (2000), no. 1, 173-199. https://doi.org/10.1007/s002229900028
  6. A. B. Givental, Equivariant Gromov-Witten invariants, Internat. Math. Res. Notices 1996 (1996), no. 13, 613-663. https://doi.org/10.1155/S1073792896000414
  7. A. B. Givental, Semisimple Frobenius structures at higher genus, Internat. Math. Res. Notices 2001 (2001), no. 23, 1265-1286. https://doi.org/10.1155/S1073792801000605
  8. T. Graber and R. V. Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999), no. 2, 487-518. https://doi.org/10.1007/s002220050293
  9. F. Janda, Relations on ${\bar{M}}_{g,n}$ via equivariant Gromov-Witten theory of ℙ1, Algebr. Geom. 4 (2017), no. 3, 311-336. https://doi.org/10.14231/AG-2017-018
  10. F. Janda, R. Pandharipande, A. Pixton, and D. Zvonkine, Double ramification cycles on the moduli spaces of curves, Publ. Math. Inst. Hautes Etudes Sci. 125 (2017), 221-266. https://doi.org/10.1007/s10240-017-0088-x
  11. A. Klemm, M. Kreuzer, E. Riegler, and E. Scheidegger, Topological string amplitudes, complete intersection Calabi-Yau spaces and threshold corrections, hep-th/0410018.
  12. Y.-P. Lee and R. Pandharipande, Frobenius manifolds, Gromov-Witten theory and Virasoro constraints, https://people.math.ethz.ch/-rahul/, 2004.
  13. H. Lho, Gromov-Witten invariants of Calabi-Yau fibrations, arXiv:1904.10315.
  14. H. Lho and R. V. Pandharipande, Stable quotients and the holomorphic anomaly equation, Adv. Math. 332 (2018), 349-402. https://doi.org/10.1016/j.aim.2018.05.020
  15. H. Lho and R. V. Pandharipande, Crepant resolution and the holomorphic anomaly equation for [ℂ3/ℤ3], Proc. Lond. Math. Soc. (3) 119 (2019), no. 3, 781-813. https://doi.org/10.1112/plms.12248
  16. A. Marian, D. Oprea, and R. V. Pandharipande, The moduli space of stable quotients, Geom. Topol. 15 (2011), no. 3, 1651-1706. https://doi.org/10.2140/gt.2011.15.1651
  17. D. Zagier and A. Zinger, Some properties of hypergeometric series associated with mirror symmetry in Modular Forms and String Duality, 163-177, Fields Inst. Commun. 54, AMS 2008. https://doi.org/10.1090/fic/054/07