Asymptotic growth of powers of ideals
Catalin Ciuperca, Florian Enescu, Sandra Spiroff
Abstract
Let A be a locally analytically unramified local ring and let J1,...,Jk,I be ideals in A. If C=C(J1,...,Jk;I) is the cone generated by the (k+1)-tuples (m1,...,mk,n) such that J1m1...Jkmk is contained in In, 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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