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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
91/2019

Multiplicity of the saturated special fiber ring of height three Gorenstein ideals

Yairon Cid Ruiz and Vivek Mukundan

Abstract

Let $R$ be a polynomial ring over a field and $I \subset R$ be a Gorenstein ideal of height three that is minimally generated by homogeneous polynomials of the same degree. We compute the multiplicity of the saturated special fiber ring of $I$. The obtained formula depends only on the number of variables of $R$, the minimal number of generators of $I$, and the degree of the syzygies of $I$. Applying results from arXiv:1805.05180, we get a formula for the $j$-multiplicity of $I$ and an effective method to study a rational map determined by a minimal set of generators of $I$.

Received:
01.10.19
Published:
03.10.19
MSC Codes:
13A30, 14E05, 13D02, 13D45

Related publications

inJournal
2021 Repository Open Access
Yairon Cid-Ruiz and Vivek Mukundan

Multiplicity of the saturated special fiber ring of height three Gorenstein ideals

In: Acta mathematica Vietnamica, 46 (2021) 4, pp. 663-674