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
MSC-Numbers: 13A30, 14E05, 13D02, 13D45
Link to arXiv: See the arXiv entry of this preprint.
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.