Chern classes and Lie-Rinehart algebras

Details Chern classes and Lie-Rinehart algebras Chern classes and Lie-Rinehart algebras

2003-06-17

arxiv.org/abs/math/0306254v2

Mathematics

Algebraic Geometry

Revised version: 10 pages, example added in section 2

Scientific paper

Classically the Chern-classes of a locally free coherent A-module W are defined using the curvature of a connection. If we more generally consider the problem of defining Chern-classes where W is a coherent A-module, a connection might not exist. In this paper we use the linear Lie-algebroid of W, where W is any coherent A-module of finite presentation, to define the first Chern-class of W. We also do explicit calculations of Chern-classes for maximal Cohen-Macaulay modules on isolated hypersurface-singularities and 2-dimensional quotient-singularities.

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