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arXiv · 1212.1419

The $j$-Multiplicity of Monomial Ideals

Jack Jeffries·Jonathan Montaño
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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.

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Jack Jeffries, Jonathan Montaño. 2012-12-06. The $j$-Multiplicity of Monomial Ideals. https://arxiv.org/abs/1212.1419

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