Singularities of moduli spaces of vector bundles over curves in characteristic \(0\) and \(p\) (Q841517)

Let \(X\) be a nonsingular projective curve over an algebraically closed field \(k\) of any characteristic. The authors consider a family of nonsingular curves \(X_W \to \text{Spec}\,W\) of genus \(g \geq 2,\) over the spectrum of the ring \(W\) of Witt vectors over \(k\) of characteristic \(p\), and relative moduli spaces \(U_W\) of (semi)stable bundles with fixed Hilbert polynomial. They investigate the specialization of \(U_W\)'s from characteristic \(0\) to characteristic \(p\). They also discuss types of singularities of these spaces.