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

Yairon Cid Ruiz and Vivek Mukundan

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Submission date: 01. Oct. 2019
Bibtex
MSC-Numbers: 13A30, 14E05, 13D02, 13D45
Link to arXiv: See the arXiv entry of this preprint.

Abstract:
Let R be a polynomial ring over a field and I ⊂ 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.