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arXiv · 1807.03189

Multiplicity of the saturated special fiber ring of height two perfect ideals

Yairon Cid-Ruiz
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Abstract

Let $R$ be a polynomial ring and $I \subset R$ be a perfect ideal of height two minimally generated by forms of the same degree. We provide a formula for the multiplicity of the saturated special fiber ring of $I$. Interestingly, this formula is equal to an elementary symmetric polynomial in terms of the degrees of the syzygies of $I$. Applying ideas introduced in arXiv:1805.05180, we obtain the value of the j-multiplicity of $I$ and an effective method for determining the degree and birationality of rational maps defined by homogeneous generators of $I$.

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Yairon Cid-Ruiz. 2018-07-09. Multiplicity of the saturated special fiber ring of height two perfect ideals. https://arxiv.org/abs/1807.03189

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