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arXiv · 1612.08213

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

Lingguang Li
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Abstract

Let $X$ be a smooth projective curve of genus $g\geq 2$ over an algebraically closed field $k$ of characteristic $p>0$, $F_X:X\rightarrow X$ 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 $(p,g)=(3,2)$.

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Lingguang Li. 2018-07-10. Frobenius Stratification of Moduli Spaces of Rank $3$ Vector Bundles in Characteristic $3$, I. https://doi.org/10.1090/tran%2F7737

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