Mathematical Research Letters

Volume 27 (2020)

Number 2

Frobenius stratification of moduli spaces of rank $3$ vector bundles in positive characteristic $3$, II

Pages: 501 – 522



Lingguang Li (School of Mathematical Sciences, Tongji University, Shanghai, China)


Let $X$ be a smooth projective curve of genus $g \geq 2$ over an algebraically closed field $k$ of characteristic $p \gt 0 , \mathfrak{M}^s_X (r, d)$ the moduli space of stable vector bundles of rank $r$ and degree $d$ on $X$. We study the Frobenius stratification of $\mathfrak{M}^s_X (3, d)$ 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 the case $(p, g) = (3, 2)$ with $3 \nmid d$.

Dedicated to the memory of Professor Michel Raynaud.

The author was partially supported by National Natural Science Foundation of China (Grant No. 11501418) and Shanghai Sailing Program.

Received 10 July 2018

Accepted 13 September 2019

Published 8 June 2020