  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.
