On symplectic resolutions and factoriality of Hamiltonian reductions
| Autor: | Travis Schedler, Gwyn Bellamy |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Large class
Factorial Pure mathematics General Mathematics Algebraic geometry Reductive group Representation theory 0101 Pure Mathematics symbols.namesake Mathematics - Algebraic Geometry 0102 Applied Mathematics symbols FOS: Mathematics Gravitational singularity Representation Theory (math.RT) Hamiltonian (quantum mechanics) Mathematics::Symplectic Geometry Algebraic Geometry (math.AG) Mathematics - Representation Theory Mathematics Symplectic geometry |
| Zdroj: | Mathematische Annalen |
| ISSN: | 0025-5831 |
| DOI: | 10.48550/arxiv.1809.04301 |
| Popis: | Recently, Herbig--Schwarz--Seaton have shown that $3$-large representations of a reductive group $G$ give rise to a large class of symplectic singularities via Hamiltonian reduction. We show that these singularities are always terminal. We show that they are $\mathbb{Q}$-factorial if and only if $G$ has finite abelianization. When $G$ is connected and semi-simple, we show they are actually locally factorial. As a consequence, the symplectic singularities do not admit symplectic resolutions when $G$ is semi-simple. We end with some open questions. Comment: 9 pages. The article has been updated to reflect the changes made by Herbig-Schwarz-Seaton to their article "Symplectic quotients have symplectic singularities" arXiv, 1706.02089 |
| Databáze: | OpenAIRE |
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