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arXiv · 2302.04472

A characterization of irreducible Hermitian symmetric spaces of tube type by $\mathbb{C}^{*}$-actions

Yingqi Liu
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Abstract

A $\mathbb{C}^{*}$-action on a projective variety $X$ is said to be of Euler type at a nonsingular fixed point $x$ if the isotropy action of $\mathbb{C}^{*}$ on $T_{x}X$ is by scalar multiplication. In this paper, it's proven that a smooth projective variety of Picard number one $X$ is isomorphic to an irreducible Hermitian symmetric space of tube type if and only if for a general pair of points $x,y$ on $X$, there exists a $\mathbb{C}^{*}$-action on $X$ which is of Euler type at $x$ and its inverse action is of Euler type at $y$.

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Yingqi Liu. 2023-02-09. A characterization of irreducible Hermitian symmetric spaces of tube type by $\mathbb{C}^{*}$-actions. https://arxiv.org/abs/2302.04472

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