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Log BPS numbers of log Calabi-Yau surfaces

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arxiv 1810.02377 v5 pith:FFPQAU2X submitted 2018-10-04 math.AG hep-th

Jinwon Choi , Michel van Garrel , Sheldon Katz , Nobuyoshi Takahashi This is my paper · ORCID
classification math.AGhep-th
keywords genusnumberscalabi-yaucountsformulasurfacesalonganalogous
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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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  1. On the log-local principle for the toric boundary

    math.AG 2019-08 conditional novelty 6.0 of 10

    For Q-factorial projective toric varieties whose toric boundary divisors are nef, the genus-zero log and local Gromov-Witten invariants with point and descendant insertions agree after the log-local normalization, and...

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