Work

Borel subgroups of the automorphism group of an affine variety

Year: 2026

Type: preprint

Abstract: We study Borel subgroups of the automorphism group of an affine variety X and their associated Lie algebras. We prove a bijective correspondence between the set of Borel subgroups of Aut(X) and the set of maximal nested unipotent subgroups of Aut(X). We show that if X is factorial of dimension at most 3, then the Lie algebra of every maximal nested unipotent subgroup has the special property of being what we call "integral"; we also show that this fails for X = affine space of dimension > 3. As an application of our results, we show that Nagata's automorphism is contained in a unique Borel subgroup.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.06664

Authors: Chitayat, Michael, Daigle, Daniel, Regeta, Andriy

Institutions: University of Padua, University of Ottawa

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7220721525

Cites: 9

Cited by:

Related to: 10