Giulia Sacca
<br>
Fibrations in abelian varieties associated to linear systems on
Enriques surfaces
<br>
I will talk about two constructions associating to a linear
system on
an Enriques surface a fibration in abelian varieties. The first
one
is the relative compactified Jacobian of the linear system and
I will
show how it leads to a smooth odd dimensional Calabi-Yau
variety. The
second construction (joint work with E. Arbarello and
A. Ferretti) is
a fibration in Prym varieties whose total space is a singular
symplectic variety. I will discuss when these singular
symplectic
varieties admit a symplectic resolution and show that, when
they do, they are
deformation equivalent to Hilb^n(K3). If time allows I talk
about how
these symplectic singularities are related to Quiver varieties.