English

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 ZZ at 0, such that OZ,0O_{Z,0} 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 alOZ,0a^l \subset O_{Z,0} 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}
}