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.

中文翻译：

---

四维圆锥辛超曲面

我们证明了每一个四维不可分解的圆锥辛超曲面与已知超曲面同构，即 Slodowy 切片 $X_n$ 横切于幂零中的 Jordan 型 $[2n-2, 1, 1]$ 的幂零轨道$\mathfrak{sp}_{2n}$ 对于一些 $n\ge 2$ 的锥体。在 Yoshinori Namikawa 所写的附录中，使用接触 Fano orbifolds 对 2 维的圆锥辛变体进行了分类。