New symplectic V-manifolds of dimension four via the relative compactified Prymian

Details New symplectic V-manifolds of dimension four via the relative compactified Prymian New symplectic V-manifolds of dimension four via the relative compactified Prymian

2007-03-06

arxiv.org/abs/math/0703168v1

Int. J. Math. 18, No. 10, 1187-1224 (2007)

Mathematics

Algebraic Geometry

28 pages

Scientific paper

Three new examples of 4-dimensional irreducible symplectic V-manifolds are constructed. Two of them are relative compactified Prymians of a family of genus-3 curves with involution, and the third one is obtained from a Prymian by Mukai's flop. They have the same singularities as two of Fujiki's examples, namely, 28 isolated singular points analytically equivalent to the Veronese cone of degree 8, but a different Euler number. The family of curves used in this construction forms a linear system on a K3 surface with involution. The structure morphism of both Prymians to the base of the family is a Lagrangian fibration in abelian surfaces with polarization of type (1,2). No example of such fibration is known on nonsingular irreducible symplectic varieties.

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