BPS invariants of symplectic log Calabi-Yau fourfolds
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- by Mohammad Farajzadeh-Tehrani;
- Trans. Amer. Math. Soc. 377 (2024), 3449-3486
- DOI: https://doi.org/10.1090/tran/9114
- Published electronically: February 14, 2024
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Abstract:
Using the Fredholm setup of Farajzadeh-Tehrani [Peking Math. J. (2023), https://doi.org/10.1007/s42543-023-00069-1], we study genus zero (and higher) relative Gromov-Witten invariants with maximum tangency of symplectic log Calabi-Yau fourfolds. In particular, we give a short proof of Gross [Duke Math. J. 153 (2010), pp. 297–362, Cnj. 6.2] that expresses these invariants in terms of certain integral invariants by considering generic almost complex structures to obtain a geometric count. We also revisit the localization calculation of the multiple-cover contributions in Gross [Prp. 6.1] and recalculate a few terms differently to provide more details and illustrate the computation of deformation/obstruction spaces for maps that have components in a destabilizing (or rubber) component of the target. Finally, we study a higher genus version of these invariants and explain a decomposition of genus one invariants into different contributions.References
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Bibliographic Information
- Mohammad Farajzadeh-Tehrani
- Affiliation: The University of Iowa, MacLean Hall, Iowa City, Iowa 52242
- MR Author ID: 999611
- ORCID: 0000-0002-2526-7153
- Email: mohammad-tehrani@uiowa.edu
- Received by editor(s): July 1, 2022
- Received by editor(s) in revised form: December 7, 2023
- Published electronically: February 14, 2024
- Additional Notes: The author was partially supported by the NSF grant DMS-2003340.
- © Copyright 2024 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 377 (2024), 3449-3486
- MSC (2020): Primary 14N35, 53D45
- DOI: https://doi.org/10.1090/tran/9114
- MathSciNet review: 4744785