01342nas a2200121   4500008004100000245007300041210006900114260001000183520091400193653004101107100002201148856005001170       2014                        en  d00aHolomorphically symplectic varieties with Prym Lagrangian fibrations0 aHolomorphically symplectic varieties with Prym Lagrangian fibrat  bSISSA3 aThe 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.10aHolomorphically symplectic varieties1 aMatteini, Tommaso  uhttp://urania.sissa.it/xmlui/handle/1963/743400974nas a2200109   4500008004100000245008800041210006900129520042300198653010900621100002200730856011200752       2014                        en  d00aAn irreducible symplectic orbifold of dimension 6 with a Lagrangian Prym  fibration0 airreducible symplectic orbifold of dimension 6 with a Lagrangian3 aA 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.10aIrreducible symplectic variety, Lagrangian fibration, Prym variety, automorphism of symplectic varieties1 aMatteini, Tommaso  uhttps://www.math.sissa.it/publication/irreducible-symplectic-orbifold-dimension-6-lagrangian-prym-fibration