12 Gennaio, 2018 15:30 in punto

Sezione di Geometria, Algebra e loro applicazioni

TROPICAL APPROACHES TO BRILL–NOETHER THEORY

Marta Panizzut, TU Berlin

Aula seminari del terzo piano

Loosely speaking, tropical geometry aims to transform algebro-geometric problems into combinatorial ones that are hopefully easier to understand. Tropical curves are connected metric graphs, and a theory of linear systems on graphs has been introduced by Baker and Norine in analogy with the one on algebraic curves. Their groundbreaking work has led to the development of a tropical Brill–Noether theory, which provides new combinatorial insights in the study of linear systems on curves. The interplay between the tropical and the classical theory is given by specialization of linear systems from the generic fiber of a 1-parameter family of curves to the dual graph of the special fiber. In this talk, I will begin by introducing the terminology and some of the
main results of this recent theory. Then I will address questions on smooth plane curves and generic smooth curves on P1 × P1 by specializing their linear systems to complete graphs and complete bipartite graphs. This based on joint works with with Filip Cools, Michele D’Adderio and
David Jensen.