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/1963/7434