Indecomposable canonical modules and connectedness
Commutative Algebra
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0211172,
title = {Indecomposable canonical modules and connectedness},
author = {Melvin Hochster and Craig Huneke},
journal= {arXiv preprint arXiv:math/0211172},
year = {2007}
}