Shatz strata in algebraic versal deformation spaces

TL;DR

This paper investigates the structure and topology of Shatz strata within algebraic versal deformation spaces of coherent sheaves on smooth complex projective curves, focusing on unstable strata and boundary behavior.

Contribution

It provides a detailed analysis of the geometry and local topology of Shatz strata, especially the large unstable ones, in the context of algebraic versal deformation spaces.

Findings

Analysis of the geometry of unstable strata

Insights into the boundary behavior of strata

Descriptions of local topological properties

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.