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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

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1435-5345
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Volume 2019, Issue 747

Issues

Rational connectivity and analytic contractibility

Morgan Brown / Tyler Foster
Published Online: 2016-07-12 | DOI: https://doi.org/10.1515/crelle-2016-0019

Abstract

Let k be an algebraically closed field of characteristic 0, and let f:XY be a morphism of smooth projective varieties over the ring k((t)) of formal Laurent series. We prove that if a general geometric fiber of f is rationally connected, then the induced map fan:XanYan between the Berkovich analytifications of X and Y is a homotopy equivalence. Two important consequences of this result are that the Berkovich analytification of any n-bundle over a smooth projective k((t))-variety is homotopy equivalent to the Berkovich analytification of the base, and that the Berkovich analytification of a rationally connected smooth projective variety over k((t)) is contractible.

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About the article

Received: 2014-07-02

Revised: 2016-03-12

Published Online: 2016-07-12

Published in Print: 2019-02-01


Funding Source: National Science Foundation

Award identifier / Grant number: DMS-0943832

Both authors are partially supported by NSF RTG grant DMS-0943832.


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2019, Issue 747, Pages 45–62, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2016-0019.

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