On the Rank of Quadratic Equations for Curves of High Degree

Research output: Contribution to journalArticlepeer-review

Abstract

Let C⊂ Pr be a linearly normal curve of arithmetic genus g and degree d. In Saint-Donat (CR Acad Sci Paris Ser A 274: 324–327, 1972), B. Saint-Donat proved that the homogeneous ideal I(C) of C is generated by quadratic equations of rank at most 4 whenever d≥ 2 g+ 2. Also, in Eisenbud et al. (Amer J Math 110: 513–539, 1988) Eisenbud, Koh and Stillman proved that I(C) admits a determinantal presentation if d≥ 4 g+ 2. In this paper, we will show that I(C) can be generated by quadratic equations of rank 3 if either g= 0 , 1 and d≥ 2 g+ 2 or else g≥ 2 and d≥ 4 g+ 4.

Original languageEnglish
Article number244
JournalMediterranean Journal of Mathematics
Volume19
Issue number6
DOIs
Publication statusPublished - 2022 Dec

Keywords

  • homogeneous ideal
  • Projective curve
  • property QR(3)

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint

Dive into the research topics of 'On the Rank of Quadratic Equations for Curves of High Degree'. Together they form a unique fingerprint.

Cite this