FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2004, VOLUME 10, NUMBER 4, PAGES 183-206

Fano direct products as rationally connected fibrations

A. V. Pukhlikov

Abstract

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Combining the connectedness principle of Shokurov and Kollár, we develop a new technique of studying birational maps of natural Fano fiber spaces. We prove that the only structures of a rationally connected fibration on direct products of typical Fano varieties are projections onto the factors. In particular, the groups of biregular and birational self-maps of Fano direct products coincide.

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Last modified: April 14, 2005