A tropical approach to the Severi problem

Abstract: Severi varieties parameterize reduced irreducible curves of given geometric genus in a given linear system on an algebraic surface. The irreducibility of Severi varieties is established firstly by Harris in 1986 for the projective plane in characteristic zero. In this talk, I will give a brief overview of the ideas involved, and describe a tropical approach to studying degererations of plane curves, which leads to a new proof of the irreducibility that also works in positive characteristic. This is joint work with Karl Christ and Ilya Tyomkin.

algebraic geometrycombinatorics

Audience: researchers in the topic

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(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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