Tropical Independence I: Shapes of Divisors and a Proof of the Gieseker-Petri Theorem

Abstract

We develop a framework to apply tropical and nonarchimedean analytic techniques to multiplication maps on linear series and study degenerations of these multiplications maps when the special fiber is not of compact type. As an application, we give a tropical criterion for a curve over a valued field to be Gieseker-Petri general.

This is an updated version of "Tropical Multiplication Maps and the Gieseker-Petri Theorem", with a new title and introduction. To appear in Algebra and Number Theory