Markushevich and Tikhomirov provided a construction of an

irreducible symplectic V-manifold of dimension 4, the relative

compactified Prym variety of a family of curves with involution, which

is a Lagrangian fibration with polarization of type (1,2). A natural

question is what the dual of this (1,2)-polarized fibration is.

Indeed, the irreducible symplectic varieties and V-manifolds with a

Lagrangian fibration are of particular interest, as they generalize K3

surfaces with elliptic pencil on one hand, and the phase spaces of

algebraically integrable systems on the other hand.

In this talk, we will answer to the question asked above. Furthermore,

we will show how the moduli space of 2-elementary K3 surfaces provides

a parametrization of the relative compactifed Prym varieties. We will

show also how it is possible to give a definition of the dual of these

varieties.

## Duality for relative Prymians associated to K3 double covers of Del Pezzo surface of degree 2

Research Group:

Grégoire Menet

Institution:

University of Lille 1

Schedule:

Thursday, April 18, 2013 - 11:00 to 12:30

Location:

A-136

Abstract: