Degenerations of amoebae and Berkovich spaces

2014/06/05 by Jonsson, Mattias · 2 citations
#14M25 #32P05 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Primary: 14T05 #Secondary: 32A60

paper · doi:10.48550/arxiv.1406.1430

Abstract

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.

Cited by

• Non-Archimedean Calabi-Yau Potentials on Certain Affine Varieties
• Continuity of the superpotentials and slices of tropical currents

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