On the topology of phase tropical varieties and beyond

Abstract: Tropical geometry is a recent area of mathematics that can be seen as a limiting aspect (or "degeneration") of algebraic geometry. For example complex curves viewed as Riemann surfaces turn to metric graphs (one dimensional combinatorial object), and $n$-dimensional complex varieties turn to $n$-dimensional polyhedral complexes with some properties.

I will first give an overview, and I will recall the definition of phase tropical varieties, their amoebas and coamoebas. After that, I will focus on non-singular algebraic curves in $(\mathbb{C}^*)^n$ with $n\geq 2$ and explain how they degenerate onto phase tropical curves that are topological manifolds. Such properties were conjectured in a talk by O. Viro in a workshop at MSRI in 2009 (Viro's conjecture is very general).

Then, I will discuss and explain how we show this fact, under certain conditions, for $k$-dimensional phase tropical variety in $(\mathbb{C}^*)^{2k}$, and I will ask some interesting questions.

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

Series comments: Please email one of the organizers to receive login info and join our mail list.