Asymptotic Behaviors of Moduli of One-dimensional Sheaves on Surfaces
Abstract
In this paper, we study the asymptotic behaviors of the Betti numbers and Picard numbers of the moduli space Mβ, of one-dimensional sheaves supported in a curve class β on S with Euler characteristic . We determine the intersection cohomology Betti numbers of Mβ, 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.
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