We develop a number of general techniques for comparing analytifications and
tropicalizations of algebraic varieties. Our basic results include a projection formula for …

This is the first in a pair of papers developing a framework for the application of logarithmic
structures in the study of singular curves of genus 1. We construct a smooth and proper …

We prove a generalisation of the Brill-Noether theorem for the variety of special divisors on a
general curve C of prescribed gonality. Our main theorem gives a closed formula for the …

We develop a number of general techniques for comparing analytifications and
tropicalizations of algebraic varieties. Our basic results include a projection formula for …

This friendly introduction to tropical geometry is meant to be accessible to first year students
in mathematics. The topics discussed here are basic tropical algebra, tropical plane curves …

In tropical geometry, given a curve in a toric variety, one defines a corresponding graph
embedded in Euclidean space. We study the problem of reversing this process for curves of …

We provide some new local obstructions to approximating tropical curves in smooth tropical
surfaces. These obstructions are based on a relation between tropical and complex …

We study whether a given tropical curve in can be realized as the tropicalization of an
algebraic curve whose non-archimedean skeleton is faithfully represented by. We give an …

We construct algebraic curves in abelian surfaces starting from tropical curves in real tori.
We give a necessary and sufficient condition for a tropical curve in a real torus to be …

For a complex toric variety $ X $ the logarithmic absolute value induces a natural retraction
of $ X $ onto the set of its non-negative points and this retraction can be identified with a …