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Yoshinori Namikawa

On deformations of ℚ-factorial symplectic varieties

Our purpose is to give a positive answer to the following problem posed in [Namikawa, Y., Extension of 2-forms and symplectic varieties, J. reine angew. Math. 539 (2001), 123– 147.]:

Problem. Let Z be a ℚ-factorial projective symplectic variety with terminal singularities. Assume that Z is smoothable by a suitable flat deformation. Is Z then non-singular from the first?

We actually prove more:

Main Theorem. Let Z be a ℚ-factorial projective symplectic variety with terminal singularities. Then any flat deformation of Z is locally trivial; in other words, it preserves all singularities on Z.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2006, 10/2006
Pages: 97 - 110

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