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

[摘要] AbstractWe 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.

[学科分类] 数学（综合）