Local BPS Invariants: Enumerative Aspects and Wall-Crossing

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

Research output: Contribution to journalArticlepeer-review


We study the BPS invariants for local del Pezzo surfaces, which can be obtained as the signed Euler characteristic of the moduli spaces of stable one-dimensional sheaves on the surface S⁠. We calculate the Poincaré polynomials of the moduli spaces for the curve classes β having arithmetic genus at most 2. We formulate a conjecture that these Poincaré polynomials are divisible by the Poincaré polynomials of ((−KS).β−1)-dimensional projective space. This conjecture motivates the upcoming work on log BPS numbers [8].
Original languageEnglish (US)
Pages (from-to)5450-5475
Number of pages26
JournalInternational Mathematics Research Notices
Issue number17
StatePublished - Sep 2020

ASJC Scopus subject areas

  • Mathematics(all)


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