Rational connectivity and analytic contractibility

Morgan Brown, Tyler Foster

Research output: Contribution to journalArticlepeer-review


Let k be an algebraically closed field of characteristic 0, and let f : X → Y 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 f an W Xan → Y an 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 Pn-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.

Original languageEnglish (US)
Pages (from-to)45-62
Number of pages18
JournalJournal fur die Reine und Angewandte Mathematik
Issue number747
StatePublished - Feb 1 2019

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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