Towards a Tropical Proof of the Gieseker-Petri Theorem
Vyassa Baratham, David Jensen, Cristina Mata, Dat Nguyen, Shalin, Parekh
TL;DR
This paper employs tropical geometry methods to prove a specific case of the Gieseker-Petri Theorem, demonstrating that most algebraic curves lack certain special linear series.
Contribution
It introduces a tropical approach to prove a case of the Gieseker-Petri Theorem, expanding the toolkit for algebraic geometry proofs.
Findings
General curves of arbitrary genus do not admit Gieseker-Petri special pencils.
Tropical techniques can be effectively used in classical algebraic geometry proofs.
Abstract
We use tropical techniques to prove a case of the Gieseker-Petri Theorem. Specifically, we show that the general curve of arbitrary genus does not admit a Gieseker-Petri special pencil.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Coding theory and cryptography · Polynomial and algebraic computation