Four-dimensional conical symplectic hypersurfaces

Ryo Yamagishi

doi:10.1016/j.jalgebra.2020.05.027

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arXiv · 1908.00684

Four-dimensional conical symplectic hypersurfaces

Ryo Yamagishi

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Abstract

We show that every indecomposable conical symplectic hypersurface of dimension four is isomorphic to the known one, namely, the Slodowy slice $X_n$ which is transversal to the nilpotent orbit of Jordan type $[2n-2, 1, 1]$ in the nilpotent cone of $\mathfrak{sp}_{2n}$ for some $n\ge 2$. In the appendix written by Yoshinori Namikawa, conical symplectic varieties of dimension two are classified by using contact Fano orbifolds.

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Ryo Yamagishi. 2019-08-02. Four-dimensional conical symplectic hypersurfaces. https://doi.org/10.1016/j.jalgebra.2020.05.027

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