Program - December 20, 2011 (Aula Dottorato, first floor)
You can download the poster and the program.
10:00-10:50
Riccardo Brasca (Università degli Studi di Milano)
$p$-adic modular forms of non-integral weight
Abstract: We recall the basic definitions of $p$-adic elliptic modular forms of integral weight, as sections of line bundles. We explain how to analytically deform these line bundles in order to obtain modular forms of non-integral weight. Finally, we consider the eigencurve, that parametrizes eigenforms. These constructions can be generalized to modular forms for other PEL shimura curves.
11:00-11:50
Sönke Rollenske (Universitët Bielefeld)
Lagrangian fibrations on irreducible holomorphic symplectic manifolds
Abstract: Irreducible holomorphic symplectic (IHS) manifolds form an important
class of manifolds with trivial canonical bundle. One fundamental aspect
of their structure theory is the question whether a given IHS manifold
admits a Lagrangian fibration. I will report on a joint project with
Daniel Greb and Christian Lehn investigating the following question of
Beauville: if a hyperkaehler manifold contains a complex torus $T$ as a
Lagrangian submanifold, does it admit a (meromorphic) Lagrangian
fibration with fibre $T$? I will describe a complete positive answer to
Beauville's Question for non-algebraic IHS manifolds, and give explicit
necessary and sufficient conditions for a positive solution in the
general case using the deformation theory of the pair $(X,T)$.
14:00-14:50
Paola Comparin (Université de Poitiers)
Van Geemen-Sarti involutions and elliptic fibrations on K3 surfaces double cover of $\mathbb P^2$
Abstract: A van Geemen-Sarti involution on a K3 surface $X$ is the translation by a 2-torsion section of an elliptic fibration on $X$. It is a symplectic involution and induces a 2-isogeny of K3 surfaces. \\
In a joint work with A. Garbagnati, we focus on K3 surfaces that are double covering of a blow up of $\mathbb P^2$ branched along rational curves and we want to classify the van Geemen-Sarti involutions on these surfaces.\\
In order to do so, we first classify the elliptic fibrations and then we analyse whether these fibrations admit a 2-torsion section. Moreover, we show how to obtain an explicit equation for the elliptic fibration.
15:00-15:50
Thomas Dedieu (Université Paul Sabatier, Toulouse)
Degeneration of K3 surfaces and applications
Abstract: I shall describe various known degenerations of K3 surfaces, and how they can be used for the study of families of curves on K3 surfaces. Among the applications, one finds existence and irreducibility results. This is based on joint work with Ciro Ciliberto.