a1 Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore (email: email@example.com)
We show that polarized endomorphisms of rationally connected threefolds with at worst terminal singularities are equivariantly built up from those on -Fano threefolds, Gorenstein log del Pezzo surfaces and 1. Similar results are obtained for polarized endomorphisms of uniruled threefolds and fourfolds. As a consequence, we show that every smooth Fano threefold with a polarized endomorphism of degree greater than one is rational.
(Received November 17 2008)
(Accepted March 04 2009)
(Online publication December 21 2009)
2000 Mathematics Subject Classification
This project is supported by an Academic Research Fund of NUS.
Dedicated to Professor M. Miyanishi on the occasion of his seventieth birthday