an:07288869
Zbl 07288869
Choi, Jinwon; van Garrel, Michel; Katz, Sheldon; Takahashi, Nobuyoshi
Log BPS numbers of log Calabi-Yau surfaces
EN
Trans. Am. Math. Soc. 374, No. 1, 687-732 (2021).
00456331
2021
j
14N35 14J33
Summary: 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.