Degenerations of amoebae and Berkovich spaces
  We prove a continuity result for the fibers of the Berkovich analytification of a complex algebraic variety with respect to the the maximum of the Archimedean norm and the trivial norm. As a consequence, we obtain generalizations of a result of Mikhalkin and Rullgard about degenerations of amoebae onto tropical varieties. 
Mattias Jonsson
math.AG math.CV