Moduli stacks of vector bundles on curves and the King–Schofield rationality proof (Pre-published version)

Abstract

Let C be a connected smooth projective curve of genus g ≥ 2 over an algebraically closed field k. Consider the coarse moduli scheme Bunr,d (resp. Bunr,L) of stable vector bundles on C with rank r and degree d ∈ Z (resp. determinant isomorphic to the line bundle L on C).