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arXiv · 1909.13633

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

Yairon Cid-Ruiz·Vivek Mukundan
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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 $I$.

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Yairon Cid-Ruiz, Vivek Mukundan. 2019-09-30. Multiplicity of the saturated special fiber ring of height three Gorenstein ideals. https://arxiv.org/abs/1909.13633

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