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Mathematics > Commutative Algebra

arXiv:1807.03189 (math)
[Submitted on 9 Jul 2018 (v1), last revised 3 May 2019 (this version, v2)]

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

Authors: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 $I$.
Comments: to appear in Proc. Amer. Math. Soc
Subjects: Commutative Algebra (math.AC); Algebraic Geometry (math.AG)
MSC classes: 13A30 (Primary), 14E05, 13D02, 13D45 (Secondary)
Cite as: arXiv:1807.03189 [math.AC]
  (or arXiv:1807.03189v2 [math.AC] for this version)
  https://doi.org/10.48550/arXiv.1807.03189

Submission history

From: Yairon Cid Ruiz [view email]
[v1] Mon, 9 Jul 2018 14:21:33 UTC (14 KB)
[v2] Fri, 3 May 2019 09:26:47 UTC (14 KB)
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