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

M. Brodmann; E. Park; P. Schenzel

doi:10.1090/S0002-9939-2010-10667-6

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

M. Brodmann, E. Park, P. Schenzel

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Let X ⊂ ℙ^r_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 ⊂ ℙ^r+1_K from a point p ε ℙ^r+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 language	English
Pages (from-to)	2025-2032
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	139
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9939-2010-10667-6
Publication status	Published - 2011 Jun

Keywords

Depth formula
Secant cone
Variety of almost minimal degree

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-2010-10667-6

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AB - 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.

KW - Depth formula

KW - Secant cone

KW - Variety of almost minimal degree

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

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Keywords

ASJC Scopus subject areas

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