Asymptotic growth of powers of ideals
Commutative Algebra
2007-05-23 v1
Abstract
Let A be a locally analytically unramified local ring and let J_1,...,J_k,I be ideals in A. If C=C(J_1,...,J_k;I) is the cone generated by the (k+1)-tuples (m_1,...,m_k,n) such that J_1^{m_1}...J_k^{m_k} is contained in I^n, we prove that the topological closure of C is a rational polyhedral cone. This generalizes results by Samuel, Nagata and Rees.
Cite
@article{arxiv.math/0610774,
title = {Asymptotic growth of powers of ideals},
author = {Catalin Ciuperca and Florian Enescu and Sandra Spiroff},
journal= {arXiv preprint arXiv:math/0610774},
year = {2007}
}
Comments
9 pages, 2 figures, to appear in Illinois J. Math