Asymptotic growth of saturated powers and epsilon multiplicity
Abstract
Asymptotic properties of saturated powers of modules over a local domain R are studied. Under mild conditions, it is shown that the limit as k goes to infinity of the quotient of the saturation of the k-th power of a module E by the k-th power of E, when divided by k^{d+e-1}, exists. Here d is the dimension of R and e is the rank of E. We deduce that under these assumptions, the epsilon multiplicity of E, defined by Ulrich and Validashti as a limsup, actually exists as a limit.
Keywords
Cite
@article{arxiv.1009.4111,
title = {Asymptotic growth of saturated powers and epsilon multiplicity},
author = {Steven Dale Cutkosky},
journal= {arXiv preprint arXiv:1009.4111},
year = {2010}
}
Comments
9 pages. In the revised version a typo ("n" changed to "k") is fixed in the statement of Corollary 1.3. A couple of new corollaries are added and some references are added. In the second revision (13 pages) some extensions from domains of depth \ge 2 are given to domains of dimension \ge 2