On some multiplicity and mixed multiplicity formulas (Forum Math. 26(2014), 413-442)

TL;DR

This paper develops additivity, reduction, and recursion formulas for mixed multiplicities of multi-graded modules and ideals, providing new tools for understanding their structure and applications to multi-graded Rees modules.

Contribution

It introduces new additivity, reduction, and recursion formulas for mixed multiplicities, extending previous results and applying them to multi-graded Rees modules.

Findings

Derived additivity and reduction formulas for mixed multiplicities.

Established recursion formulas for the sum of mixed multiplicities.

Applied formulas to compute multiplicities of multi-graded Rees modules.

Abstract

This paper gives the additivity and reduction formulas for mixed multiplicities of multi-graded modules $M$ and mixed multiplicities of arbitrary ideals, and establishes the recursion formulas for the sum of all the mixed multiplicities of $M.$ As an application of these formulas we get the recursion formulas for the multiplicity of multi-graded Rees modules.