Delzant models of moduli spaces

A. N. Tyurin

Izvestiya. Mathematics , Tome 67 (2003) no. 2, pp. 365-376

Résumé

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 $M_\Sigma(2,0)$ of semistable topologically trivial vector bundles of rank 2 on an algebraic curve $\Sigma$ of genus $g$ there is a holomorphic isomorphism $f\colon M_\Sigma(2,0)\setminus K_g\to DM_g \setminus D$, where $K_g$ is the Kummer variety of the Jacobian of $\Sigma$, sending the polarization of $DM_g$ to the theta divisor of the moduli space. This isomorphism induces isomorphisms of the spaces $H^0(M_\Sigma(2,0),\Theta^k)$ and $H^0(DM_g,H^k)$.