Multiplicity of the Saturated Special Fiber Ring of Height Three Gorenstein Ideals

Let R be a polynomial ring over a field and let 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 o...

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Bibliographic Details
Published in:Acta mathematica vietnamica 2021-12, Vol.46 (4), p.663-674
Main Authors: Cid-Ruiz, Yairon, Mukundan, Vivek
Format: Article
Language:English
Subjects:
Generators
Mathematics
Mathematics and Statistics
Polynomials
Rings (mathematics)
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Summary:Let R be a polynomial ring over a field and let 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 Busé et al. (Proc. Lond. Math. Soc. 121 (4):743–787, 2020 ) 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 .
ISSN:0251-4184
2315-4144
DOI:10.1007/s40306-020-00410-1