On deformations of ℚ-factorial symplectic varieties

By Y. Namikawa. 2005

57 citations recorded by the source corpus.

Abstract 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/eed830b78f9da33b52c3780287968182826f896d

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In Geometry and Topology

1. A. Rapagnetta
2. Giovanni Mongardi
3. A. Perego
4. M. Shen
5. Charles Vial

In Mathematical Physics

1. Giovanni Mongardi
2. A. Rapagnetta
3. A. Perego
4. M. Shen
5. Charles Vial

Citations in the corpus

• Monodromy and birational geometry of O'Grady's sixfolds (2019, background): “In both cases, H(X,Z) has a pure Hodge structure with a compatible deformation invariant quadratic form BX , the Beauville-Bogomolov form in the smooth case and the Beauville-Bogomolov-Namikawa form in the singular case (see [27]).”