English

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