Isolated torus invariants and automorphism groups of rigid varieties

2020/07/15 by Viktoria Borovik, Borovik, Viktoria, Sergey Gaifullin +1
Mathematics · #14R05 #14R20 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Primary 14J50 #Secondary 13A50

paper · pdf · doi:10.48550/arxiv.2007.07882

openalex publication_date 2020/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Perepechko and Zaidenberg conjectured that the neutral component of the automorphism group of a rigid affine variety is a torus. We prove this conjecture for toric varieties and varieties with a torus action of complexity one. We also obtain a criterion for an m-suspension over a rigid variety to be rigid (for every rigid variety and every regular function). Additionally, we study the automorphism group of m-suspensions satisfying this criterion.

Related

• Automorphisms of rigid hypersurfaces with separable variables
• Automorphisms of nonnormal toric varieties
• Varieties with a torus action of complexity one having a finite number of automorphism group orbits
• Characterization of affine surfaces with a torus action by their automorphism groups
• On the automorphism group of a toral variety