On completely decomposable defining equations of finite sets in Pn

Jaeheun Jung, Euisung Park

Research output: Contribution to journalArticlepeer-review


Let (Formula presented.) be the homogeneous ideal of a finite set Γ in (Formula presented.) of d points in linearly general position. In 1972, Saint-Donat proved that if (Formula presented.) then (Formula presented.) is generated by completely decomposable quadratic polynomials. Later, R. Treger generalized this result by showing that (Formula presented.) is generated by forms of degree (Formula presented.) if (Formula presented.) for some (Formula presented.). This paper aims to generalize Saint-Donat’s work in a different direction by proving that the degree m piece of (Formula presented.) can be generated by completely decomposable forms of degree m if and only if (Formula presented.). Communicated by Daniel Erman.

Original languageEnglish
Pages (from-to)2527-2533
Number of pages7
JournalCommunications in Algebra
Issue number6
Publication statusPublished - 2024

Bibliographical note

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  • Completely decomposable form
  • defining equations of a finite set
  • linearly general position

ASJC Scopus subject areas

  • Algebra and Number Theory


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