Asymptotic Behaviors of Moduli of One-dimensional Sheaves on Surfaces
Fei Si, Feinuo Zhang · arXiv (Cornell University) · 2024
In this paper, we study the asymptotic behaviors of the Betti numbers and Picard numbers of the moduli space $M_{β,χ}$ of one-dimensional sheaves supported in a curve class $β$ on $S$ with Euler characteristic $χ$. We determine the intersection cohomology Betti numbers of $M_{β,χ}$ when $S$ is a del Pezzo surface and $β$ is sufficiently positive. As an application, we formulate a $P = C$ conjecture regarding the refined BPS invariants for local del Pezzo surfaces.