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 $3 \nmid d$.

中文翻译：

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正特征$ 3 $中II级秩为$ 3 $的向量束的模空间的Frobenius分层

设$ X $为特征$ p \ gt 0的\ a代数闭合域$ k $上属$ g \ geq 2 $的光滑投影曲线，\ mathfrak {M} ^ s_X（r，d）$在$ X $上的等级$ r $和等级$ d $的稳定向量束。我们用稳定向量束的Frobenius后卫的Harder-Narasimhan多边形研究$ \ mathfrak {M} ^ s_X（3，d）$的Frobenius分层，并获得每个非空Frobenius层的不可约性和维数情况$（p，g）=（3，2）$且$ 3 \ nmid d $。