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math.AG2025
Tropical limit of hyperbolic amoebas of complex analytic surfaces
Peter Petrov, Mikhail Shkolnikov
In this letter, we establish a general fact about the convergence of images of families of closed analytic surfaces in the special linear group un…
math.AG2025
Introduction to phase tropicalization
Mikhail Shkolnikov, Peter Petrov
The usual approach to tropical geometry is via degeneration of amoebas of algebraic subvarieties of an algebraic torus . An amoeba is logarithmic projection of th…
math.AG2025
tropicalization and lines on surfaces
Mikhail Shkolnikov, Peter Petrov
The paper is based on a talk given by the first author at the Gökova Geometry \& Topology conference in May 2024. The subject is an interplay between the ideas of tropical geometry…