Characterizing rational homogeneous spaces via $\mathbb{C}^*$-actions

Gianluca Occhetta; Luis E. Solá Conde

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arXiv · 2405.05654

Characterizing rational homogeneous spaces via $\mathbb{C}^*$-actions

Gianluca Occhetta·Luis E. Solá Conde

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Abstract

We study smooth varieties of Picard number one admitting a special dominating family of rational curves and an equalized $\mathbb{C}^*$-action. In particular we show that $X$ is a smooth variety of Picard number one with nef tangent bundle admitting an equalized $\mathbb{C}^*$-action with an isolated extremal fixed point if and only if $X$ is an irreducible Hermitian symmetric space.

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Gianluca Occhetta, Luis E. Solá Conde. 2024-05-09. Characterizing rational homogeneous spaces via $\mathbb{C}^*$-actions. https://arxiv.org/abs/2405.05654

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