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Title: BPS invariants of symplectic log Calabi-Yau fourfolds
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.  more » « less
Award ID(s):
2003340
PAR ID:
10542535
Author(s) / Creator(s):
Publisher / Repository:
Transactions of AMS
Date Published:
Journal Name:
Transactions of the American Mathematical Society
ISSN:
0002-9947
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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