Delzant models of moduli spaces

Abstract

For every genus g, we construct a smooth, complete, rational polarized algebraic variety DM_g together with a normal crossing divisor D = sum D_i, such that for every moduli space M_C(2,0) of semistable topologically trivial vector bundles of rank 2 on an algebraic curve C of genus g there exists a holomorphic isomorphism f: M_C(2,0) minus K_2 -> DM_g minus D, where K_2 is the Kummer variety of the Jacobian of C, sending the polarization of DM_g to the theta divisor of the moduli space. This isomorphism induces isomorphisms of the spaces of conformal blocks.