Indecomposable canonical modules and connectedness

Details Indecomposable canonical modules and connectedness Indecomposable canonical modules and connectedness

2002-11-11

arxiv.org/abs/math/0211172v1

Mathematics

Commutative Algebra

Scientific paper

The purpose of this paper is to prove a generalization of Faltings' connectedness theorem which asserts that, for a complete local domain R of dimension n, the punctured spectrum of R/I is connected if the ideal I is generated by at most n-2 elements. We replace the condition that R be a domain by the requirement that the canonical module of R be indecomposable. We also study equivalent conditions for the canonical module to be indecomposable; under mild conditions this is equivalent to the S_2-ification of the local ring to be local.

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