Additions to a theorem of Morey-Ulrich

Thiago Fiel; Zaqueu Ramos; Aron Simis

Additions to a theorem of Morey-Ulrich

Commutative Algebra 2025-09-10 v2

Authors: Thiago Fiel , Zaqueu Ramos , Aron Simis

Abstract

Let $R = k[x_1,\ldots, x_d]$ denote a standard graded polynomial ring over an algebraically closed field $k$ , and let $I \subset R$ be a perfect ideal of codimension $2$ with an $n\times (n-1)$ linear presentation matrix $\phi$ . We prove an extended formulation of a theorem of Morey and Ulrich in the case where $I$ satisfies condition $G_{d-1}$ , but not condition $G_d$ .

Keywords

perfect ideal linear presentation matrix condition G_d Morey-Ulrich theorem commutative algebra

Cite

@article{arxiv.2505.03065,
  title  = {Additions to a theorem of Morey-Ulrich},
  author = {Thiago Fiel and Zaqueu Ramos and Aron Simis},
  journal= {arXiv preprint arXiv:2505.03065},
  year   = {2025}
}

Comments

In this version, we've made several changes to the article's introduction and exposition. We've corrected some typos found in the previous version

Additions to a theorem of Morey-Ulrich

Abstract

Keywords

Cite

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