Fano-Mori elementary contractions with reducible general fiber

Occhetta, Gianluca; Panizzolo, Davide

Kodai Math. J., Tome 28 (2005) no. 1, p. 559-576 / Harvested from Project Euclid

Résumé

Let φ: X → W be an elementary divisorial Fano-Mori contraction from a smooth projective variety, defined by a linear system |m(K_X + 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.

Publié le : 2005-10-14
Classification:

@article{1134397769,
     author = {Occhetta, Gianluca and Panizzolo, Davide},
     title = {Fano-Mori elementary contractions with reducible general fiber},
     journal = {Kodai Math. J.},
     volume = {28},
     number = {1},
     year = {2005},
     pages = { 559-576},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1134397769}
}

Occhetta, Gianluca; Panizzolo, Davide. Fano-Mori elementary contractions with reducible general fiber. Kodai Math. J., Tome 28 (2005) no. 1, pp.  559-576. http://gdmltest.u-ga.fr/item/1134397769/