  By results of the author there exists a projective (holomorphic) symplectic
desingularization of the moduli space of rank-two torsion-free sheaves on a
genus-two Jacobian with $c_1=0$ and $c_2=2$. This desingularization has a
natural map to the self-product of the Jacobian. We show that the fiber over
$(0,0)$ is a 6-dimensional projective irreducible symplectic variety (and hence
a 12-dimensional compact Hyperkahler manifold) with second Betti number equal
to 8. Thus it is not deformation equivalent to any of the (few) known examples
of irreducible symplectic varieties, even up to birational equivalence.
