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arXiv · 1406.7312

Rational Connectivity and Analytic Contractibility

Morgan Brown·Tyler Foster
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Abstract

Let k be an algebraically closed field of characteristic 0, and let f be a morphism of smooth projective varieties from X to Y over the ring k((t)) of formal Laurent series. We prove that if a general geometric fiber of f is rationally connected, then the Berkovich analytifications of X and Y are homotopy equivalent. Two important consequences of this result are that the homotopy type of the Berkovich analytification of any smooth projective variety X over k((t)) is a birational invariant of X, and that the Berkovich analytification of a rationally connected smooth projective variety over k((t)) is contractible.

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Morgan Brown, Tyler Foster. 2014-06-27. Rational Connectivity and Analytic Contractibility. https://arxiv.org/abs/1406.7312

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