%0 Thesis
%D 2014
%T Holomorphically symplectic varieties with Prym Lagrangian fibrations
%A Tommaso Matteini
%K Holomorphically symplectic varieties
%X The thesis presents a construction of singular holomorphically symplectic varieties as Lagrangian fibrations. They are relative compactified Prym varieties associated to curves on symplectic surfaces with an antisymplectic involution. They are identified with the fixed locus of a symplectic involution on singular moduli spaces of sheaves of dimension 1. An explicit example, giving a singular irreducible symplectic 6-fold without symplectic resolutions, is described for a K3 surface which is the double cover of a cubic surface. In the case of abelian surfaces, a variation of this construction is studied to get irreducible symplectic varieties: relative compactified 0-Prym varieties. A partial classification result is obtained for involutions without fixed points: either the 0-Prym variety is birational to an irreducible symplectic variety of K3[n]-type, or it does not admit symplectic resolutions.
%I SISSA
%G en
%U http://urania.sissa.it/xmlui/handle/1963/7434
%1 7511
%2 Mathematics
%4 1
%# MAT/03
%$ Submitted by Tommaso Matteini (tommatte@sissa.it) on 2014-09-15T12:25:24Z
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%0 Report
%D 2014
%T An irreducible symplectic orbifold of dimension 6 with a Lagrangian Prym fibration
%A Tommaso Matteini
%K Irreducible symplectic variety, Lagrangian fibration, Prym variety, automorphism of symplectic varieties
%X A new example of an irreducible symplectic variety of dimension 6, with only finite quotient singularities, is described as a relative compactified Prymian of a family of genus 4 curves with involution. It is associated to a K3 surface which is a double cover of a cubic surface. It has a natural Lagrangian fibration in abelian 3-folds with polarization type (1,1,2). It does not admit any symplectic resolution.
%G en
%1 7360
%2 Mathematics
%4 1
%# MAT/03 GEOMETRIA
%$ Submitted by Tommaso Matteini (tommatte@sissa.it) on 2014-04-07T21:56:09Z
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