RULED SURFACES WITH NON-TRIVIAL SURJECTIVE ENDOMORPHISMS

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Duration: 3 min 30 s
Description: Let X be a non-singular ruled surface over an algebraically closed field of characteristic zero. There is a non-trivial surjective endomorphism f :X →X if and only if X is (1) a toric surface, (2) a P1-bundle over an elliptic curve, or (3) the direct product of P1 and a non-singular curve up to finite étale coverings.
Noboru Nakayama
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