Tropicalization of Severi varieties

MARÍA ISABEL HERRERO; ALICIA DICKENTEIN; LUIS TABERA

Berkeley, California

Seminario; Computational Algebraic Geometry Seminar; 2014

Departamento de Matemática, Universidad de Berkeley

Severi varieties are classical objects of Algebraic geometry. In this talk, we will concentrate on the Severi varieties given as the closure of the set of univariate polynomials with degree n and two nodes. I will introduce some necessary basic notions of Tropical geometry and present a full description of all the cones of the tropicalization of the Severi variety as sets in $mathbb{R}^{n+1}$. The structure of theses cones depends on combinatorial and arithmetic ingredients. According to this description, we will see that some but not all of these cones are from the secondary fan. This talk is based on joint work with Alicia Dickenstein and Luis Tabera.