On multiplicities of graded sequences of ideals
Commutative Algebra
2007-05-23 v1 Algebraic Geometry
Abstract
We generalize a result of Ein-Lazarsfeld-Smith (math.AG/0202303), proving that for an arbitrary sequence of zero-dimensional ideals, the multiplicity of the sequence is equal with its volume. This is done using a deformation to monomial ideals. As a consequence of our result, we obtain a formula which computes the multiplicity of an ideal I in terms of the multiplicities of the initial monomial ideals of the powers I^m. We use this to give a new proof of the inequality between multiplicity and the log canonical threshold due to de Fernex, Ein and the author.
Keywords
Cite
@article{arxiv.math/0203235,
title = {On multiplicities of graded sequences of ideals},
author = {Mircea Mustata},
journal= {arXiv preprint arXiv:math/0203235},
year = {2007}
}
Comments
AMS-LaTeX, 21 pages