## Kodai Mathematical Journal

### Fano-Mori elementary contractions with reducible general fiber

#### Abstract

Let φ: XW be an elementary divisorial Fano-Mori contraction from a smooth projective variety, defined by a linear system |m(KX + τL)|, with L a φ-ample line bundle in Pic(X), τ a positive integer and m » 0.

General fibers of such contractions are known to be irreducible if τ ≥ dim X − 3 (and so if dim X ≤ 4). We prove that, if τ ≥ dim X − 4, except possibly for one case, a general non trivial fiber is irreducible.

The special case, which can occur when dim X = 5, is effective, as we show by an example in the last section of the paper.

#### Article information

Source
Kodai Math. J., Volume 28, Number 3 (2005), 559-576.

Dates
First available in Project Euclid: 12 December 2005

https://projecteuclid.org/euclid.kmj/1134397769

Digital Object Identifier
doi:10.2996/kmj/1134397769

Mathematical Reviews number (MathSciNet)
MR2194546

Zentralblatt MATH identifier
1121.14013

#### Citation

Occhetta, Gianluca; Panizzolo, Davide. Fano-Mori elementary contractions with reducible general fiber. Kodai Math. J. 28 (2005), no. 3, 559--576. doi:10.2996/kmj/1134397769. https://projecteuclid.org/euclid.kmj/1134397769