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

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

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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.

Originele taal-2	Engels
Pagina's (van-tot)	200-229
Aantal pagina's	30
Tijdschrift	ACM Communications in Computer Algebra
Volume	57
Nummer van het tijdschrift	4
DOI's	https://doi.org/10.1145/3653002.3653004
Status	Gepubliceerd - 15 mrt. 2024

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

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A Proof of the Brill-Noether Method from Scratch

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