Work

Symbols at infinity and Lie algebras of vector fields

Year: 2026

Type: preprint

Abstract: If $X$ is smooth projective complex variety, $D$ is a simple normal crossings divisor and $A$ an ample divisor with support $D$, then there is an associated filtration of the Lie algebra of on the affine variety $U=X\setminus D$ induced from the subspaces $T_X(\log D)(nA)\subset T_U.$ We show that the associated graded Lie algebra is finitely generated in a strong sense. We deduce as a consequence that vector fields on any smooth affine variety form a finitely generated Lie algebra.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.25973

Author: Bouaziz, Emile

Institutions: Fudan University, Shanghai Institute for Mathematics and Interdisciplinary Sciences

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214108329

Cites: 4

Cited by: 1

Related to: 10