Compactifications of moduli of $G$-bundles and conformal blocks

Abstract

For a stable curve of genus g ≥ 2 and simple, simply connected group G, we show that sections of determinant of cohomology on the stack of G-bundles extend to the normalization of its closure in the stack of Schmitt's honest singular G-bundles. We use this to show that the conformal blocks algebra A on M g is finitely generated and that closed fibers of Proj A → M g can be interpreted as normalized moduli spaces of singular G-bundles.