%0 Journal Article
%T Rational Connectivity and Analytic Contractibility
%A Morgan Brown
%A Tyler Foster
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1406.7312v1