Mathematical Research Letters
Volume 20 (2013)
The $j$-multiplicity of monomial ideals
Pages: 729 – 744
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.