Asymptotic Behaviors of Moduli of One-dimensional Sheaves on Surfaces

Fei Si; Feinuo Zhang

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arXiv · 2406.11512

Asymptotic Behaviors of Moduli of One-dimensional Sheaves on Surfaces

Fei Si·Feinuo Zhang

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Abstract

In this paper, we study the asymptotic behaviors of the Betti numbers and Picard numbers of the moduli space $M_{\beta,\chi}$ of one-dimensional sheaves supported in a curve class $\beta$ on $S$ with Euler characteristic $\chi$. We determine the intersection cohomology Betti numbers of $M_{\beta,\chi}$ when $S$ is a del Pezzo surface and $\beta$ is sufficiently positive. As an application, we formulate a $P = C$ conjecture regarding the refined BPS invariants for local del Pezzo surfaces.

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BibTeX RIS

Fei Si, Feinuo Zhang. 2024-06-17. Asymptotic Behaviors of Moduli of One-dimensional Sheaves on Surfaces. https://arxiv.org/abs/2406.11512

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