On surfaces of minimal degree in P5

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Abstract

There are exactly four surfaces of minimal degree in P5, up to projective equivalence. And they have the same graded Betti numbers. So it is a natural question to ask how to recognize them by their defining equations. In this paper we provide an answer to this question in terms of the rank loci of quadratic equations of those four surfaces. We show that the sets of rank 3 and rank 4 quadratic equations distinguish them.

Original languageEnglish
Pages (from-to)116-123
Number of pages8
JournalJournal of Symbolic Computation
Volume109
DOIs
Publication statusPublished - 2022 Mar 1

Keywords

  • Rank of quadratic equation
  • Surfaces of minimal degree

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics

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