On varieties of almost minimal degree II: A rank-depth formula

M. Brodmann, E. Park, P. Schenzel

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Let X ⊂ ℙrK 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+1K from a point p ε ℙr+1K\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
Issue number6
Publication statusPublished - 2011 Jun


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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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