On varieties of almost minimal degree II

A rank-depth formula

M. Brodmann, Euisung Park, P. Schenzel

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Let X ⊂ ℙr K denote a variety of almost minimal degree other than a normal del Pezzo variety. Then X is the projection of a rational normal scroll X̃ ⊂ ℙr+1 K from a point p ε ℙr+1 K\X̃. We show that the arithmetic depth of X can be expressed in terms of the rank of the matrix M′(p), where M′ is the matrix of linear forms whose 3 × 3 minors define the secant variety of X̃.

Original languageEnglish
Pages (from-to)2025-2032
Number of pages8
JournalProceedings of the American Mathematical Society
Volume139
Issue number6
DOIs
Publication statusPublished - 2011 Jun 1

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Secant Varieties
Linear Forms
del operator
M-matrix
Minor
Projection
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Keywords

  • Depth formula
  • Secant cone
  • Variety of almost minimal degree

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

On varieties of almost minimal degree II : A rank-depth formula. / Brodmann, M.; Park, Euisung; Schenzel, P.

In: Proceedings of the American Mathematical Society, Vol. 139, No. 6, 01.06.2011, p. 2025-2032.

Research output: Contribution to journalArticle

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