Asymptotic growth of powers of ideals

Details Asymptotic growth of powers of ideals Asymptotic growth of powers of ideals

2006-10-26

arxiv.org/abs/math/0610774v1

Mathematics

Commutative Algebra

9 pages, 2 figures, to appear in Illinois J. Math

Scientific paper

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.

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