Rationality of rationally connected threefolds admitting non-isomorphic endomorphisms

Details Rationality of rationally connected threefolds admitting non-isomorphic endomorphisms Rationality of rationally connected threefolds admitting non-isomorphic endomorphisms

2010-11-08

arxiv.org/abs/1011.1705v1

Mathematics

Algebraic Geometry

Transactions of the American Mathematical Society, to appear; 21 pages

Scientific paper

We prove a structure theorem for non-isomorphic endomorphisms of weak Q-Fano threefolds, or more generally for threefolds with 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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