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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
3/2020

Mixed multiplicities and projective degrees of rational maps

Yairon Cid Ruiz

Abstract

We consider the notion of mixed multiplicities for multigraded modules by using Hilbert series, and this is later applied to study the projective degrees of rational maps. We use a general framework to determine the projective degrees of a rational map via a computation of the multiplicity of the saturated special fiber ring. As specific applications, we provide explicit formulas for all the projective degrees of rational maps determined by perfect ideals of height two or by Gorenstein ideals of height three.

Received:
Jan 5, 2020
Published:
Jan 8, 2020
MSC Codes:
13H15, 14E05

Related publications

inJournal
2021 Repository Open Access
Yairon Cid-Ruiz

Mixed multiplicities and projective degrees of rational maps

In: Journal of algebra, 566 (2021), pp. 136-162