Tropical independence I: Shapes of divisors and a proof of the Gieseker–Petri theorem

By David Jensen, Sam Payne. 2014

66 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/364d7b1eebf1593dc5cf2c906e79c3ed9408681f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. David Jensen
2. Dhruv Ranganathan
3. Matthew Baker
4. Omid Amini
5. Lucia Caporaso
6. Sam Payne
7. Joseph Rabinoff
8. Melody Chan

In Geometry and Topology

1. David Jensen
2. Dhruv Ranganathan
3. Matthew Baker
4. Omid Amini
5. Laura Demarco
6. Lucia Caporaso
7. Sam Payne
8. Melody Chan

In Statistical and Nonlinear Physics

1. Dhruv Ranganathan
2. David Jensen
3. Matthew Baker

Citations in the corpus

• Degeneration of Linear Series from the Tropical Point of View and Applications (2015, methodology): “[JP14] Let D be a divisor on a metric graph Γ, with f1, .”
• Brill-Noether theory for curves of a fixed gonality (2017, methodology): “The material of this section is developed in detail in those papers and their precursors [20, 30].”