A Proof of the Brill-Noether Method from Scratch-Reference-Cited by-同舟云学术

A Proof of the Brill-Noether Method from Scratch

Published:2023-12 Issue:4 Volume:57 Page:200-229
ISSN:1932-2240
Container-title:ACM Communications in Computer Algebra
language:en
Short-container-title:ACM Commun. Comput. Algebra

Author:

Berardini Elena¹,Couvreur Alain²,Lecerf Grégoire³

Affiliation:

1. CNRS; Institut de Mathématiques de Bordeaux, Université de Bordeaux, Talence, France and Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, the Netherlands

2. Inria & Laboratoire d'informatique de l'École polytechnique, CNRS, École polytechnique, Institut Polytechnique de Paris, Palaiseau, France

3. Laboratoire d'informatique de l'École polytechnique, CNRS, École polytechnique, Institut Polytechnique de Paris, Palaiseau, France

Abstract

In 1874 Brill and Noether designed a seminal geometric method for computing bases of Riemann-Roch spaces. From then, their method has led to several algorithms, some of them being implemented in computer algebra systems. The usual proofs often rely on abstract concepts of algebraic geometry and commutative algebra. In this paper we present a short self-contained and elementary proof that mostly needs Newton polygons, Hensel lifting, bivariate resultants, and Chinese remaindering.

Publisher

Association for Computing Machinery (ACM)

Link

https://dl.acm.org/doi/pdf/10.1145/3653002.3653004

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