Moduli Spaces of Sheaves on General Blow-ups of ℙ²

2022/08/07 by Junyan Zhao, Zhao, Junyan
Computer Science · Mathematics · #14D20 #14F05 #14J26 #14J60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2208.03619

openalex publication_date 2022/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be the blow-up of ℙ² along m general points, and A=H-∑ ε_iE_i be a generic polarization with 0<ε_i≪1. We classify the Chern characters which satisfy the weak Brill-Noether property, i.e. a general sheaf in M_A(\bfv), the moduli space of slope stable sheaves with Chern character \bfv, has at most one non-zero cohomology. We further give a necessary and sufficient condition for the existence of stable sheaves. Our strategy is to specialize to the case when the m points are collinear.

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