1,232 research outputs found
Symplectic singularities
We discuss a particular class of rational Gorenstein singularities, which we
call symplectic. A normal variety V has symplectic singularities if its smooth
part carries a closed symplectic 2-form whose pull-back in any resolution X -->
V extends to a holomorphic 2-form on X . Our main result is the classification
of isolated symplectic singularities with smooth projective tangent cone. They
are in one-to-one correspondence with simple complex Lie algebras: to a Lie
algebra g corresponds the singularity at 0 of the closure of the minimal
(nonzero) nilpotent adjoint orbit in g .Comment: 9 pages, Plain Te
Antisymplectic involutions of holomorphic symplectic manifolds
Let X be a holomorphic symplectic manifold, of dimension divisible by 4, and
s an antisymplectic involution of X . The fixed locus F of s is a Lagrangian
submanifold of X ; we show that its \^A-genus is 1. As an application, we
determine all possibilities for the Chern numbers of F when X is a deformation
of the Hilbert square of a K3 surface.Comment: Final version, accepted for publication by the Journal of Topolog
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