Eyal Markman, University of Massachusetts, Amherst

Modular Galois covers associated to symplectic resolutions of singularities

Let Y be a normal projective variety and p a morphism from X to Y, which is a projective holomorphic symplectic resolution. Namikawa proved that the Kuranishi deformation spaces Def(X) and Def(Y) are both smooth, of the same dimension, and p induces a finite branched cover f from Def(X) to Def(Y). We prove that f is Galois. When X is simply connected, and its holomorphic symplectic structure is unique, up to a scalar factor, then the Galois group is a product of Weyl groups of finite type. We consider generalizations of the above set-up, where Y is affine symplectic, or a Calabi-Yau threefold with a curve of ADE-singularities.

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