Characterizing quasi-affine spherical varieties via the automorphism group

2019/11/25 by Andriy Regeta, Regeta, Andriy, Immanuel van Santen +1
Mathematics · #14J50 #14M27 #14R20 #22F50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1911.10896

openalex publication_date 2019/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a connected reductive algebraic group. In this note we prove that for a quasi-affine G-spherical variety the weight monoid is determined by the weights of its non-trivial \mathbbG_a-actions that are homogeneous with respect to a Borel subgroup of G. As an application we get that a smooth affine G-spherical variety that is non-isomorphic to a torus is determined by its automorphism group inside the category of smooth affine irreducible varieties.

Citations

• Lifting of morphisms to quotient presentations

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