Small contractions of smooth varieties

Gianluca Occhetta

Vol. 208 (2003), No. 1, 125–149

DOI: 10.2140/pjm.2003.208.125

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.

Milestones

Received: 24 May 2001

Revised: 22 October 2001

Published: 1 January 2003