arXiv subjects

Feinuo Zhang

Publications and source records attributed to Feinuo Zhang.

4 recordsLinked to original sources

arXiv2025

Stabilization of intersection Betti numbers for moduli spaces of one-dimensional sheaves on surfaces

In this paper, we develop a unified approach to study the intersection Betti numbers of moduli spaces of one-dimensional semistable sheaves on smooth projective surfaces. Assuming the irreducibility of such moduli spaces, we prove that their intersection Betti numbers in a certain range of degrees coincide with the stable Betti numbers of Hilbert schemes of points. As an application, for surfaces with nef anticanonical divisor, we show that these intersection Betti numbers stabilize in each fixed degree, which fits into the broader context of stable cohomology for moduli spaces of sheaves; if in addition the moduli spaces are smooth, we also prove a refined stabilization result on perverse Hodge numbers.

math.AG↗

arXiv2025

On the Picard numbers of moduli spaces of one-dimensional sheaves on surfaces

Motivated by asymptotic phenomena of moduli spaces of higher rank stable sheaves on algebraic surfaces, we study the Picard number of the moduli space of one-dimensional stable sheaves supported in a sufficiently positive divisor class on a surface. We give an asymptotic lower bound of the Picard number in general. In some special cases, we show that this lower bound is attained based on the geometry of moduli spaces of stable pairs and relative Hilbert schemes of points. Additionally, we discuss several related questions and provide examples where the asymptotic irreducibility of the moduli space fails, highlighting a notable distinction from the higher rank case.

math.AG↗

arXiv2024

Cohomological stabilization, perverse filtrations, and refined BPS invariants for del Pezzo surfaces

We prove an asymptotic product formula for the refined BPS invariants associated with a local del Pezzo surface. Our formula governs the cohomological stabilization of the perverse filtration on the intersection cohomology of the moduli space of 1-dimensional semistable sheaves on a del Pezzo surface. Combined with the theory of Fourier transform of Maulik--Shen--Yin, we show that the perverse filtration matches asymptotically with the Chern filtration defined via tautological classes. In the case of the projective plane, our results resolve conjectures of Kononov--Pi--Shen.

math.AG↗

arXiv2024

Asymptotic Behaviors of Moduli of One-dimensional Sheaves on Surfaces

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.

math.AG↗