Program - December 17, 2019 (Aula C, second floor)
You can download the poster and the program.
14:00-14:50
Thorsten Beckmann
Birational Geometry of moduli spaces of stable objects on Enriques surfaces
Abstract:
The geometry of K3 and Enriques surfaces is deepy intertwined. In this talk, we study this connection for the moduli spaces of stable objects. Using wall-crossing for K3 surfaces obtained by Bayer and Macri', we employ Chow-theoretic results to deduce similiar statements for Enriques surfaces. Applications to the birational geometry of the moduli spaces will be discussed.
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15:00-15:50
Vladimiro Benedetti
The geometry of the Coble cubic
Abstract:
The Coble cubic is the unique cubic in the projective space P^8 whose
singular locus is a given abelian surface A. Its geometry has been
studied, among others, by Beauville, Ortega, Dolgachev, Nguyen. It has
been proven that its projective dual (a sextic hypersurface) is directly
related to a moduli space of sheaves on a curve of genus 2, whose Jacobian
is A itself. By using the language of orbital degeneracy loci, we are able
to enrich the geometric description of these varieties. In particular, we
will show how to construct the Kummer fourfold associated to A and how to
describe the law group of A in a strikingly similar way to the description
of the low group of plane cubics.
This is a joint work with Laurent Manivel and Fabio Tanturri.
16:30-17:20
Irene Spelta
Infinitely many totally geodesic subvarieties via Galois covering of elliptic curves
Abstract:
We will speak about totally geodesic subvarieties of A_g which are generically contained in the Torelli locus. Coleman-Oort conjecture says that for genus g large enough such varieties should not exist.
Nevertheless if $g\leq7$ there are examples obtained as families of Jacobians of Galois coverings of curves f:C -> C', where C' is a smooth curve of genus g'. All of them satisfy a sufficient condition, which we will denote by (*).
We will describe this condition. First, it gives us a bound on the genus g' which we use to say that there are only 6 families of Galois coverings of curves of $g'\geq1$ which yield Special subvarieties of A_g.
Then we use (*) again to study the Prym maps of the families described above: we will prove that they are fibered, via their Prym map, in curves which are totally geodesic. In this way we get infinitely many new examples of totally geodesic subvarieties of A_2, A_3, A_4.