Frobenius Stratification of Moduli Spaces of Rank $3$ Vector Bundles in Characteristic $3$, I

Abstract

Let $X$ be a smooth projective curve of genus $g\ge 2$ over an algebraically closed field $k$ of characteristic $p>0$, $F_X:X\to X$ the absolute Frobenius morphism. Let $\M^s_X(r,d)$ be the moduli space of stable vector bundles of rank $r$ and degree $d$ on $X$. We study the Frobenius stratification of $\M^s_X(3,0)$ 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 the case $(p,g)=(3,2)$.

arXiv comment18 pages. All comments are welcome

References in corpus (5)

• Direct images of bundles under Frobenius morphisms
• Moduli of Vector Bundles on Curves in Positive Characteristics
• A stratification of the moduli space of vector bundles on curves
• Stability of sheaves of locally closed and exact forms
• Maximally Frobenius-destabilized vector bundles over smooth algebraic curves

Cited by in corpus (1)

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