Mixed Multiplicities of Maximal Degrees (J. Korean Math. Soc. 55 (2018), No. 3, 605-622)

TL;DR

This paper broadens the concept of mixed multiplicities to include maximal terms in the Hilbert polynomial, providing more general and natural results than the original theory.

Contribution

It introduces a new class of mixed multiplicities focusing on maximal polynomial terms, expanding and refining the existing theory.

Findings

Defines a broader class of mixed multiplicities.

Provides general and natural results extending the original theory.

Enhances understanding of Hilbert polynomial's maximal terms.

Abstract

The original mixed multiplicity theory considered the class of mixed multiplicities concerning the terms of highest total degree in the Hilbert polynomial. This paper defines a broader class of mixed multiplicities that concern the maximal terms in this polynomial, and gives many results, which are not only general but also more natural than many results in the original mixed multiplicity theory.