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 …

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 …

One of the main goals of tropical geometry is to study classical algebraic geometry with the
help of simpler objects. Locally these objects are polyhedral complexes equipped with extra …

We determine the tropicalizations of very affine surfaces over a valued field that are obtained
from del Pezzo surfaces of degree 5, 4 and 3 by removing their (− 1)-curves. On these …

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 …

Smooth tropical cubic surfaces are parametrized by maximal cones in the unimodular
secondary fan of the triple tetrahedron. There are 344\, 843\, 867 344 843 867 such cones …

We give an overview of recently implemented polymake features for computations in tropical
geometry. The main focus is on explicit examples rather than technical explanations. Our …

Let E be a plane in an algebraic torus (K^*)^ n (K∗) n over an algebraically closed field K.
Given a balanced 1-dimensional fan C in the tropicalization of E, ie in the Bergman fan of the …

The classical statement of Cayley-Salmon that there are 27 lines on every smooth cubic
surface in P^ 3 fails to hold under tropicalization: a tropical cubic surface in TP^ 3 often …

A degeneration of algebraic counting problems to tropical geometry produces new concepts
and computational approaches. The challenge is to find methods to lift the results in the …