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arXiv · 1810.02377

Log BPS numbers of log Calabi-Yau surfaces

Jinwon Choi·Michel van Garrel·Sheldon Katz·Nobuyoshi Takahashi
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Abstract

Let $(S,E)$ be a log Calabi-Yau surface pair with $E$ a smooth divisor. We define new conjecturally integer-valued counts of $\mathbb{A}^1$-curves in $(S,E)$. These log BPS numbers are derived from genus 0 log Gromov-Witten invariants of maximal tangency along $E$ via a formula analogous to the multiple cover formula for disk counts. A conjectural relationship to genus 0 local BPS numbers is described and verified for del Pezzo surfaces and curve classes of arithmetic genus up to 2. We state a number of conjectures and provide computational evidence.

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Jinwon Choi, Michel van Garrel, Sheldon Katz, Nobuyoshi Takahashi. 2018-10-04. Log BPS numbers of log Calabi-Yau surfaces. https://arxiv.org/abs/1810.02377

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