Bernstein-Kouchnirenko-Khovanskii with a symmetry

Abstract: A generic polynomial $f(x,y,z)$ with a prescribed Newton polytope defines a symmetric spatial curve $f(x,y,z)=f(y,x,z)=0$. We shall study its geometry, and classify the Newton polytopes for which this geometry is exceptional. As a motivating application, we shall classify generic one-parameter families of complex univariate polynomials, whose Galois group differs from the complete symmetric group. We shall see how some of these results conjecturally extend to higher dimensions and more complicated symmetries. This is based on joint work with Lionel Lang.

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