### 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 |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

## Fingerprint Dive into the research topics of 'On varieties of almost minimal degree II: A rank-depth formula'. Together they form a unique fingerprint.

## Cite this

Brodmann, M., Park, E., & Schenzel, P. (2011). On varieties of almost minimal degree II: A rank-depth formula.

*Proceedings of the American Mathematical Society*,*139*(6), 2025-2032. https://doi.org/10.1090/S0002-9939-2010-10667-6