Comparison of symbolic and ordinary powers of ideals
Commutative Algebra
2009-11-07 v1
Abstract
In this paper we generalize the theorem of Ein-Lazarsfeld-Smith (concerning the behavior of symbolic powers of prime ideals in regular rings finitely generated over a field of characteristic 0) to arbitrary regular rings containing a field. The basic theorem states that in such rings, if P is a prime ideal of height c, then for all n, the symbolic (cn)th power of P is contained in the nth power of P. Results are also given in the non-regular case: one must correct by a power of the Jacobian ideal in rings where the Jacobian ideal is defined.
Keywords
Cite
@article{arxiv.math/0211174,
title = {Comparison of symbolic and ordinary powers of ideals},
author = {Melvin Hochster and Craig Huneke},
journal= {arXiv preprint arXiv:math/0211174},
year = {2009}
}