Shatz strata in algebraic versal deformation spaces

2022/07/25 by Yinbang Lin, Lin, Yinbang
Mathematics · #14D15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary: 14D20 #Secondary: 14B05

paper · pdf · doi:10.48550/arxiv.2207.11853

openalex publication_date 2022/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Over a smooth complex projective curve, we study an algebraic versal deformation space with fixed determinant of a coherent sheaf. The algebraic versal deformation space decomposes into a disjoint union of Shatz strata, namely locally closed subschemes which parametrize coherent sheaves with common Harder-Narasimhan types. We study the geometry and local topology of large unstable strata and their behavior along boundaries.

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