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arXiv · 1809.04301

On symplectic resolutions and factoriality of Hamiltonian reductions

Gwyn Bellamy·Travis Schedler
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Abstract

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.

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Gwyn Bellamy, Travis Schedler. 2018-09-12. On symplectic resolutions and factoriality of Hamiltonian reductions. https://arxiv.org/abs/1809.04301

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