PreprintCC BY 4.0arXiv
Symbols at infinity and Lie algebras of vector fields
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∖ D induced from the subspaces TX(log D)(nA)⊂ TU. 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.
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BibTeX
@misc{bouaziz2026symbols,
title = {{Symbols at infinity and Lie algebras of vector fields}},
author = {Emile Bouaziz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25973},
eprint = {2609.25973},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25973},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Symbols at infinity and Lie algebras of vector fields
AU - Emile Bouaziz
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25973
UR - https://arxiv.org/abs/2609.25973
AB - 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∖ D induced from the subspaces T_X(log D)(nA)⊂ 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.
ER -