Rationality of rationally connected threefolds admitting non-isomorphic endomorphisms

Zhang, De-Qi

doi:10.1090/S0002-9947-2012-05500-0

Rationality of rationally connected threefolds admitting non-isomorphic endomorphisms
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Trans. Amer. Math. Soc. 364 (2012), 6315-6333 Request permission

Abstract:

We prove a structure theorem for non-isomorphic endomorphisms of weak $\mathbb {Q}$-Fano threefolds or, more generally, for threefolds with a big anti-canonical divisor. Also provided is a criterion for a fibred rationally connected threefold to be rational. As a consequence, we show (without using the classification) that every smooth Fano threefold having a non-isomorphic surjective endomorphism is rational.

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