Description:

Title: Infinitesimal structure of Bun_G

Abstract: Given a semisimple group G and a smooth projective curve X over an algebraically closed field of arbitrary characteristic, let Bun_G(X) denote the moduli space of principal G-bundles over X. For a bundle P without infinitesimal symmetries, we describe the n^th order divided-power infinitesimal jet spaces of Bun_G(X) at P for each n. The description is in terms of differential forms on the Fulton-Macpherson compactification of the configuration space, with logarithmic singularities along the diagonal divisor. We also briefly discuss applications into constructing Hitchin's flat connection on the vector bundle of conformal blocks.