Frobenius Stratification of Moduli Spaces of Vector Bundles in Positive characteristic. II

TL;DR

This paper investigates the structure of moduli spaces of stable vector bundles over algebraic curves in positive characteristic, focusing on Frobenius stratification and its geometric properties, including irreducibility and dimension in specific cases.

Contribution

It introduces a detailed analysis of Frobenius stratification on moduli spaces, providing new results on irreducibility and dimension for particular parameters.

Findings

Irreducibility of Frobenius strata in certain cases

Dimension calculations for Frobenius strata

Description of Harder-Narasimhan polygons in the stratification

Abstract

Let $X$ be a smooth projective curve of genus $g(X)\geq 1$ over an algebraically closed field $k$ of characteristic $p>0$, $\M^s_X(r,d)$ the moduli space of stable vector bundles of rank $r$ and degree $d$ on $X$. We study the Frobenius stratification of $\M^s_X(r,d)$ in terms of Harder-Narasimhan polygons of Frobenius pull backs of stable vector bundles and obtain the irreducibility and dimension of each non-empty Frobenius stratum in case $(p,g,r)=(3,2,3)$.