Polarized endomorphisms of uniruled varieties (with Appendix by Y. Fujimoto and N. Nakayama)

Details Polarized endomorphisms of uniruled varieties (with Appendix by Y. Fujimoto and N. Nakayama) Polarized endomorphisms of uniruled varieties (with Appendix by Y. Fujimoto and N. Nakayama)

2009-03-06

arxiv.org/abs/0903.1256v1

Mathematics

Algebraic Geometry

Compositio Mathematica (to appear)

Scientific paper

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 P^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 > 1, is rational.

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