Globally F-regular type of moduli spaces (Q2205570)

Let \(k\) be an algebraically closed field of characteristic zero. A variety \(V\) over the field \(k\) is of globally \(F\)-regular type if its modulo \(p\) reduction \(V_p\) is globally \(F\)-regular. Suppose \(C\) is an irreducible projective curve over the field \(k\) with utmost one node. In this paper, the authors prove that the moduli space \(\mathcal{U}_C(\omega, L)\) of semistable parabolic bundles (with parabolic structure \(\omega\)) with fixed determinant \(L\) is of globally \(F\)-regular type if \(C\) is smooth. When the curve \(C\) has exactly one node, there is a notion of the moduli space of semistable generalised parabolic sheaves \(\mathcal{P}_\omega\) on the normalisation \(\tilde{C}\) of \(C\). The authors also prove that the fixed determinant space \(\mathcal{P}_\omega^L\) is of globally \(F\)-regular type.