A Proof of the Brill-Noether Method from Scratch

Elena Berardini; Alain Couvreur; Grégoire Lecerf

doi:10.1145/3653002.3653004

A Proof of the Brill-Noether Method from Scratch

Elena Berardini, Alain Couvreur, Grégoire Lecerf

Mathematical Communication Theory

Research output: Contribution to journal › Article › Academic › peer-review

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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.

Original language	English
Pages (from-to)	200-229
Number of pages	30
Journal	ACM Communications in Computer Algebra
Volume	57
Issue number	4
DOIs	https://doi.org/10.1145/3653002.3653004
Publication status	Published - 15 Mar 2024

Bibliographical note

Publisher Copyright:
© 2024 Copyright is held by the owner/author(s).

Keywords

algebraic curves
Brill-Noether method
Hensel lemmas
Newton polygons
Riemann-Roch spaces

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10.1145/3653002.3653004

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A Proof of the Brill-Noether Method from Scratch

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Keywords

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