Mathematics

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.