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On deformations of Q-factorial symplectic varieties

Yoshinori Namikawa
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Abstract

We shall prove that any small deformation of a Q-factorial projective symplectic variety with terminal singularities is locally rigid; in other words, it preserves the singularity. In particular, many singular symplectic moduli of semi-stable sheaves on K3 have no smoothings via deformations. As an application of the result, we also prove that the smootheness is preserved under a flop in our symplectic case. We conjecture that a projective symplectic variety has a smoothing by a flat deformation if and only if it has a crepant (symplectic) resolution. This conjecture would be true if the minimal model conjecture were true.

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Yoshinori Namikawa. 2005-09-09. On deformations of Q-factorial symplectic varieties. https://arxiv.org/abs/math/0506534

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