English

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.

Keywords

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