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On the complex formed by contracting differential forms with a vector field on a hypersurface singularity

Giraldo Suárez, Luis and Gómez-Mont, Xavier (2001) On the complex formed by contracting differential forms with a vector field on a hypersurface singularity. Boletín de la Sociedad Matemática Mexicana, 7 (2). pp. 211-221. ISSN 1405-213X

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Abstract

Let (V, 0) subset of (Cn+1, 0) bean analytic hypersurface with an isolated singularity at 0, and X = (X) over tilde \(V) a tangent vector field to V, where (X) over tilde is a holomorphic vector field in (Cn+1, 0) which has an isolated singularity at 0, The homological index of X at 0 can be defined ([4]) as the Euler characteristic of the complex formed by contracting with X the Kahler differentials on V. In that complex, the homology groups are equidimensional and isomorphic to certain modules defined from the finite dimensional C-algebras associated to the jacobian ideal of the function defining V, and to the coordinates of (X) over tilde ([4]). In this paper, we present an algorithm that provides those isomorphisms in an explicit way, so making it possible to face the problem of extending the homological index to other geometric situations ([3]).


Item Type:Article
Uncontrolled Keywords:holomorphic vector fields on singular hypersurfaces; index of holomorphic vector fields; Koszul complex and regular sequences
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:16668
Deposited On:10 Oct 2012 08:26
Last Modified:10 Oct 2012 08:26

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