TY - THES
T1 - Holomorphically symplectic varieties with Prym Lagrangian fibrations
Y1 - 2014
A1 - Tommaso Matteini
KW - Holomorphically symplectic varieties
AB - 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.
PB - SISSA
UR - http://urania.sissa.it/xmlui/handle/1963/7434
U1 - 7511
U2 - Mathematics
U4 - 1
U5 - MAT/03
ER -
TY - RPRT
T1 - An irreducible symplectic orbifold of dimension 6 with a Lagrangian Prym fibration
Y1 - 2014
A1 - Tommaso Matteini
KW - Irreducible symplectic variety, Lagrangian fibration, Prym variety, automorphism of symplectic varieties
AB - 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.
U1 - 7360
U2 - Mathematics
U4 - 1
U5 - MAT/03 GEOMETRIA
ER -