Equivariant Slices for Symplectic Cones
| Autor: | Travis Schedler |
|---|---|
| Přispěvatelé: | National Science Foundation |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Noncommutative ring General Mathematics 010102 general mathematics Algebraic geometry 01 natural sciences Representation theory 0101 Pure Mathematics Mathematics - Algebraic Geometry Mathematics - Symplectic Geometry Product (mathematics) 0103 physical sciences FOS: Mathematics Equivariant map Symplectic Geometry (math.SG) 010307 mathematical physics Uniqueness 0101 mathematics Representation Theory (math.RT) Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Quotient Mathematics - Representation Theory Mathematics Symplectic geometry |
| Popis: | The Darboux-Weinstein decomposition is a central result in the theory of Poisson (degenerate symplectic) varieties, which gives a local decomposition at a point as a product of the formal neighborhood of the symplectic leaf through the point and a formal slice. Recently, conical symplectic resolutions, and more generally, Poisson cones, have been very actively studied in representation theory and algebraic geometry. This motivates asking for a C*-equivariant version of the Darboux-Weinstein decomposition. In this paper, we develop such a theory, prove basic results on their existence and uniqueness, study examples (quotient singularities and hypertoric varieties), and applications to noncommutative algebra (their quantization). We also pose some natural questions on existence and quantization of C*-actions on slices to conical symplectic leaves. Comment: 39 pages, final version |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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