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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Rationality of rationally connected threefolds admitting non-isomorphic endomorphisms


Author: De-Qi Zhang
Journal: Trans. Amer. Math. Soc. 364 (2012), 6315-6333
MSC (2010): Primary 14E20, 14J45, 14E08, 32H50
Published electronically: June 29, 2012
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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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Additional Information

De-Qi Zhang
Affiliation: Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076, Singapore
Email: matzdq@nus.edu.sg

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05500-0
PII: S 0002-9947(2012)05500-0
Keywords: Endomorphism, rationally connected variety, rationality of variety
Received by editor(s): September 18, 2009
Received by editor(s) in revised form: September 25, 2010
Published electronically: June 29, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.