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Polarized endomorphisms of uniruled varieties. With an appendix by Y. Fujimoto and N. Nakayama

Published online by Cambridge University Press:  21 December 2009

De-Qi Zhang*
Affiliation:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore (email: matzdq@nus.edu.sg)
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Abstract

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We show that polarized endomorphisms of rationally connected threefolds with at worst terminal singularities are equivariantly built up from those on ℚ-Fano threefolds, Gorenstein log del Pezzo surfaces and ℙ1. 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.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2009

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