### 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 | |

Publication status | Published - 2011 Jun 1 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*139*(6), 2025-2032. https://doi.org/10.1090/S0002-9939-2010-10667-6

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

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 139, no. 6, pp. 2025-2032. https://doi.org/10.1090/S0002-9939-2010-10667-6

}

TY - JOUR

T1 - On varieties of almost minimal degree II

T2 - A rank-depth formula

AU - Brodmann, M.

AU - Park, Euisung

AU - Schenzel, P.

PY - 2011/6/1

Y1 - 2011/6/1

N2 - 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.

AB - 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.

KW - Depth formula

KW - Secant cone

KW - Variety of almost minimal degree

UR - http://www.scopus.com/inward/record.url?scp=79952120948&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952120948&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2010-10667-6

DO - 10.1090/S0002-9939-2010-10667-6

M3 - Article

VL - 139

SP - 2025

EP - 2032

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 6

ER -