Rational connectivity and analytic contractibility

Morgan Brown, Tyler Foster

Research output: Contribution to journalArticle

Abstract

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
Volume2019
Issue number747
DOIs
StatePublished - Feb 1 2019

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Contractibility
Connectivity
Projective Variety
Fibers
Homotopy Equivalence
Laurent Series
Morphism
Algebraically closed
Homotopy
Bundle
Fiber
Ring

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Rational connectivity and analytic contractibility. / Brown, Morgan; Foster, Tyler.

In: Journal fur die Reine und Angewandte Mathematik, Vol. 2019, No. 747, 01.02.2019, p. 45-62.

Research output: Contribution to journalArticle

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