A Brian\c{c}on-Skoda type result for a non-reduced analytic space
Complex Variables
2015-02-25 v3 Commutative Algebra
Algebraic Geometry
Abstract
We present here an analogue of the Brian\c{c}on-Skoda theorem for a germ of an analytic space at 0, such that is Cohen-Macaulay, but not necessarily reduced. More precisely, we find a sufficient condition for membership of a function in a power of an arbitrary ideal in terms of size conditions of Noetherian differential operators applied to that function. This result generalizes a theorem by Huneke in the reduced case.
Keywords
Cite
@article{arxiv.1001.0322,
title = {A Brian\c{c}on-Skoda type result for a non-reduced analytic space},
author = {Jacob Sznajdman},
journal= {arXiv preprint arXiv:1001.0322},
year = {2015}
}