2014/07/29 by Fabrizio Donzelli, Donzelli, Fabrizio
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons #math.AG
paper · pdf · doi:10.48550/arxiv.1407.7824
arxiv created 2014/07/29 · openalex publication_date 2014/07/29 · arxiv updated 2014/07/30 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
For a smooth manifold X equipped with a volume form, let \dL be the Lie algebra of volume preserving smooth vector fields on X. A. Lichnerowicz proved that the abelianization of \dL is a finite-dimensional vector space, and that its dimension depends only on the topology of X. In this paper we provide analogous results for some classical examples of non-singular complex affine algebraic varieties that admit a nowhere-zero algebraic form of top degree (which plays the role of a volume form).