The $j$-Multiplicity of Monomial Ideals
Commutative Algebra
2020-04-14 v3 Combinatorics
Abstract
We prove a characterization of the j-multiplicity of a monomial ideal as the normalized volume of a polytopal complex. Our result is an extension of Teissier's volume-theoretic interpretation of the Hilbert-Samuel multiplicity for m-primary monomial ideals. We also give a description of the epsilon-multiplicity of a monomial ideal in terms of the volume of a region.
Keywords
Cite
@article{arxiv.1212.1419,
title = {The $j$-Multiplicity of Monomial Ideals},
author = {Jack Jeffries and Jonathan Montaño},
journal= {arXiv preprint arXiv:1212.1419},
year = {2020}
}
Comments
14 pages, 4 figures. Final Version