Frobenius splitting of moduli spaces of parabolic bundles

Abstract

Let $C$ be a nonsingular projective curve over an algebraically closed field of characteristic $p>0$ and $I\subset C$ be a finite set. If ${\mathcal{U}}_{C,\omega }$ denotes the moduli space of semistable parabolic bundles of rank $r$ and degree $d$ on $C$ with parabolic structures determined by $\omega =(k,\{\vec{n}(x),\vec{a}(x){\}}_{x\in I})$, we prove that ${\mathcal{U}}_{C,\omega }$ is \textit{$F$-split} for generic $C$ and generic choice of $I$ when $p>3r$.

arXiv comment42 pages