A characterization of irreducible Hermitian symmetric spaces of tube type by ℂ^*-actions

2023/02/09 by Yingqi Liu, Liu, Yingqi
Mathematics · Medicine · #14L30 (Primary) 14M17 #14M27 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Phytoestrogen effects and research

paper · pdf · doi:10.48550/arxiv.2302.04472

openalex publication_date 2023/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A 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 ℂ^* on T_xX 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 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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