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

Cited by in corpus (24)

• Tropical independence II: The maximal rank conjecture for quadrics
• Tropical Ideals
• Embeddings and immersions of tropical curves
• The Kodaira dimensions of ${\overline{\mathcal{M}}}_{22}$ and ${\overline{\mathcal{M}}}_{23}$
• Global Brill--Noether Theory over the Hurwitz Space
• Prym-Brill-Noether Loci of special curves
• The Gieseker-Petri theorem and imposed ramification
• Limit linear series and ranks of multiplication maps
• Stability of Normal Bundles of Space Curves
• The distribution of Weierstrass points on a tropical curve
• Combinatorial and inductive methods for the tropical maximal rank conjecture
• On the strong maximal rank conjecture in genus 22 and 23
• Smoothing of Limit Linear Series of Rank One on Saturated Metrized Complexes of Algebraic Curves
• The non-abelian Brill-Noether divisor on ${\overline{\mathcal{M}}}_{13}$ and the Kodaira dimension of ${\overline{\mathcal{R}}}_{13}$
• Recent Developments in Brill-Noether Theory
• Quiver representations arising from degenerations of linear series, I
• The automorphism group of $M_{0,n}^{\text{trop}}$ and ${\overline{M}}_{0,n}^{\text{trop}}$
• Smoothing of limit linear series on curves and metrized complexes of pseudocompact type
• Chip-firing groups of iterated cones
• Scrollar Invariants of Tropical Curves
• Degenerations of amoebae and Berkovich spaces
• Brill-Noether loci with ramification at two points
• Lifting divisors with imposed ramifications on a generic chain of loops
• Voronoi tilings, toric arrangements and degenerations of line bundles III