Stratifying the moduli space of stable vector bundles by decomposition type

TL;DR

This paper studies the stratification of the moduli space of stable vector bundles by decomposition type, providing dimension estimates and insights into the structure of these moduli spaces, especially over smooth projective curves.

Contribution

It introduces a stratification of the moduli space based on decomposition type and derives sharp dimension estimates for these strata, advancing understanding of their geometric structure.

Findings

Dimension estimates for strata on smooth projective curves

Sharp bounds for the closure of prime-to-p trivializable bundles

Insights into the structure of the moduli space in characteristic p

Abstract

The moduli space of slope-stable vector bundles on a normal projective variety over an algebraically closed field of characteristic $p\geq 0$ is stratified with respect to the decomposition type. On a smooth projective curve of genus at least 2 we obtain mostly sharp dimension estimates for these strata. As an application, we obtain a dimension estimate for the closure of the prime to p trivializable stable bundles in the moduli space of stable vector bundles.