Abstract:
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 $H^0(DM_g,H^k)$.
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