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

References in corpus (5)

• The tropicalization of the moduli space of curves
• Canonical representatives for divisor classes on tropical curves and the Matrix-Tree Theorem
• The Brill-Noether rank of a tropical curve
• Involutions on standard Young tableaux and divisors on metric graphs
• A simple characteristic-free proof of the Brill-Noether theorem

Cited by in corpus (25)

• 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
• Limit linear series and ranks of multiplication maps
• The Gieseker-Petri theorem and imposed ramification
• Prym-Brill-Noether Loci of special curves
• The distribution of Weierstrass points on a tropical curve
• Stability of Normal Bundles of Space Curves
• On the strong maximal rank conjecture in genus 22 and 23
• Combinatorial and inductive methods for the tropical maximal rank conjecture
• Smoothing of Limit Linear Series of Rank One on Saturated Metrized Complexes of Algebraic Curves
• Topology of nonarchimedean analytic spaces and relations to complex algebraic geometry
• Recent Developments in Brill-Noether Theory
• Quiver representations arising from degenerations of linear series, I
• The non-abelian Brill-Noether divisor on ${\overline{\mathcal{M}}}_{13}$ and the Kodaira dimension of ${\overline{\mathcal{R}}}_{13}$
• 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
• Brill-Noether loci with ramification at two points
• Voronoi tilings, toric arrangements and degenerations of line bundles III
• Lifting divisors with imposed ramifications on a generic chain of loops
• Chip-firing groups of iterated cones
• Degenerations of amoebae and Berkovich spaces
• Scrollar Invariants of Tropical Curves