Integrality of relative BPS state counts of toric del Pezzo surfaces
Integrality of relative BPS state counts of toric del Pezzo surfaces
Relative Bogomolny-Prasad-Sommerfield (BPS) state counts for log Calabi-Yau surface pairs were introduced by Gross-Pandharipande-Siebert in [4] and conjectured by the authors to be integers.For toric del Pezzo surfaces, we provide an arithmetic proof of this conjecture, by relating these invariants to the local BPS state counts of the surfaces.The latter …