Abstract

Let ϕ : X → W be a proper surjective map from a smooth complex projective variety X to a normal variety W; if ϕ has connected fibers and −K_X is ϕ-ample, ϕ is called a Fano-Mori contraction; if ϕ is an isomorphism in codimension 2, then ϕ is called a small contraction.

In this paper we study Fano-Mori contractions with fibers covered by large families of rational curves. After some general results we specialize to the case of small contractions, giving a complete description of small contractions of fivefolds with smooth fibers and relatively spanned anticanonical bundle.

Authors