Let φ:
X→
W be an elementary divisorial Fano-Mori contraction from a smooth projective variety, defined by a linear system
|m(
KX+τ
L)
|, 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 effctive, as we show by an example in the last section of the paper.
View full abstract