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

Part of: Birational geometry Holomorphic mappings and correspondences Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  21 December 2009

De-Qi Zhang
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.

Keywords

polarized endomorphismuniruled varietyrationality of variety

MSC classification

Secondary: 14E20: Coverings 14J45: Fano varieties 14E08: Rationality questions 32H50: Iteration problems
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 1 , January 2010 , pp. 145 - 168
Copyright
Copyright © Foundation Compositio Mathematica 2009

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