Log BPS numbers of log Calabi-Yau surfaces

Jinwon Choi, Michel Van Garrel, Sheldon Katz, Nobuyoshi Takahashi

Research output: Contribution to journalArticlepeer-review


Let (S,E) be a log Calabi-Yau surface pair with E a smooth divisor. We define new conjecturally integer-valued counts of A1-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

Original languageEnglish (US)
Pages (from-to)687-732
Number of pages46
JournalTransactions of the American Mathematical Society
Issue number1
StatePublished - Jan 2021

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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