Weierstrass sets on finite graphs

Abstract: Weiestrass points and Weierstrass semigroups are classical objects of study in Algebraic Geometry. The problem of determining which semigroups arise as Weierstrass semigroups of a curve goes back to Hurwitz in 1893. After the advent of tropical geometry, a divisor theory on graphs was developed by Baker and Norine, and later extended to metric graphs (namely, abstract tropical curves) by Gathmann and Kerber, and Mikhalkin and Zharkov. In this talk we present two natural tropical analogues of Weierstrass semigroups on graphs, called rank and functional Weierstrass sets, first appeared in a work of Kang, Matthews and Peachey. We present some results on these two objects and their interplay.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html