Michele Bolognesi - Humboldt Universitat zu Berlin
Moduli of vector bundles and GIT quotients.
Let C be a smooth genus g algebraic curve, with $g>1$ and
$SU_C(r)$ the moduli space of rank r semistable vector bundles
with trivial determinant on C. In this talk we will show that
$SU_C(r)$ is birational to a fibration whose fibers are
isomorphic to the GIT quotient $(\PP^{r-1})^{rg}/PGL(r)$ and
whose base is a $P^{g(r-1)}$. As an application of our results
we show that the Coble hypersurfaces are birational to
fibrations in classical modular varieties. The Coble quartic
is a fibration in Segre Cubics over $P^3$ whereas the
Coble-Dolgachev sextic is a fibration in Igusa quartics over
$P^4$. We will also discuss how these constructions could lead
to a proof of the rationality of $SU_C(r)$. These results come
from a joint work with A.Alzati and a forthcoming work with
S.Brivio.