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arXiv · 2206.13589

BPS invariants of symplectic log Calabi-Yau fourfolds

Mohammad Farajzadeh-Tehrani
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Abstract

Using the Fredholm setup of [12], 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 [23, Conjecture 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 [23, Proposition 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.

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Mohammad Farajzadeh-Tehrani. 2022-06-27. BPS invariants of symplectic log Calabi-Yau fourfolds. https://arxiv.org/abs/2206.13589

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