Automorphism groups of toroidal horospherical varieties

Lorenzo Barban; DongSeon Hwang; Minseong Kwon

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arXiv · 2602.07879

Automorphism groups of toroidal horospherical varieties

Lorenzo Barban·DongSeon Hwang·Minseong Kwon

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Abstract

We establish a structure theorem for the connected automorphism groups of smooth complete toroidal horospherical varieties, that is, toric fibrations over rational homogeneous spaces. The key ingredient is a characterization of the Demazure roots of toric fibers that extend to the total space. In particular, we provide a criterion for the reductivity of the connected automorphism groups of such varieties. As an application, we prove the K-unstability of certain $\mathbb{P}^1$-bundles over rational homogeneous spaces.

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Lorenzo Barban, DongSeon Hwang, Minseong Kwon. 2026-02-08. Automorphism groups of toroidal horospherical varieties. https://arxiv.org/abs/2602.07879

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