Delzant models of moduli spaces

For every genus g we construct a smooth, complete, rational polarized algebraic variety (DM_g,H) together with an effective normal crossing divisor D=cup-D_i such that for every moduli space M_Σ(2,0) of semistable topologically trivial vector bundles of rank 2 on an algebraic curve Σ of genus g there is a holomorphic isomorphism f: M_Σ(2,0)/K_g→DM_g/D, where K_g is the Kummer variety of the Jacobian of Σ, sending the polarization of DM_g to the theta divisor of the moduli space. This isomorphism induces isomorphisms of the spaces H⁰(M_Σ(2,0),Θ^k) and H⁰(DM_g,H^k)