A note on symplectic singularities

By Y. Namikawa. 2001

51 citations recorded by the source corpus.

In this paper we shall prove that the singular locus of a symplectic singularity has no codimension 3 irreducible components. As a corollary, a symplectic singularity is terminal if and only if its singular locus has codimension $\geq 4$. It is hoped that a symplectic singularity has much stronger properties.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/638b449c78ce21854dde398d010d8808a551daf7

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Deformations of symplectic singularities and orbit method for semisimple Lie algebras (2016, background): “roof. In the proof we can assume that Gis semisimple and simply connected. Let X˜ be a Q-terminalization of X. Assume, ﬁrst, that P = {0}. Then X has no codimension 2 leaves. By a result of Namikawa, [N1], Xis terminal. Also H2(Xreg,C) = {0} and hence H2(O,C) = {0}. Let χ∈ O, then H2(O,C) equals Hom”
Yangians and quantizations of slices in the affine Grassmannian (2012, background): “a symplectic form on its smooth locus implies that it has symplectic singularities. Since we have a Poisson map Gr~λ µ →Gr λ µ, this variety also has symplectic singularities. By a result of Namikawa [N1], this regularity in codimension 3 also implies that Gr~λ µ is terminal. Since each local singul”