The canonical ring of a stacky curve

2015/01/19 by John Voight, Voight, John, David Zureick-Brown +1 · 5 citations
Mathematics · #11F11 #14Q05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1501.04657

openalex publication_date 2015/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Generalizing the classical theorems of Max Noether and Petri, we describe generators and relations for the canonical ring of a stacky curve, including an explicit Gröbner basis. We work in a general algebro-geometric context and treat log canonical and spin canonical rings as well. As an application, we give an explicit presentation for graded rings of modular forms arising from finite-area quotients of the upper half-plane by Fuchsian groups.

Cited by

• Frobenius generation for algebraic stacks
• Wild Stacky Curves and Rings of Mod p Modular Forms
• Mumford-type Shimura curves contained in the Torelli locus
• Uniformization as Tannakian Reconstruction
• Fermat descent

Related

• Wild Stacky Curves and Rings of Mod p Modular Forms
• On the Canonical Ring of Covers of Surfaces of Minimal Degree
• Artin-Schreier-Witt Theory for Stacky Curves
• Half canonical rings of Gorenstein spin curves of genus two
• On the canonical ring of curves and surfaces