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The canonical ring of a stacky curve
About this Title
John Voight and David Zureick-Brown
Publication: Memoirs of the American Mathematical Society
Publication Year:
2022; Volume 277, Number 1362
ISBNs: 978-1-4704-5228-5 (print); 978-1-4704-7094-4 (online)
DOI: https://doi.org/10.1090/memo/1362
Published electronically: March 28, 2022
Keywords: Canonical rings,
canonical embeddings,
stacks,
algebraic curves,
modular forms,
automorphic forms,
generic initial ideals,
Gröbner bases
Table of Contents
Chapters
- 1. Introduction
- 2. Canonical rings of curves
- 3. A generalized Max Noether’s theorem for curves
- 4. Canonical rings of classical log curves
- 5. Stacky curves
- 6. Rings of modular forms
- 7. Canonical rings of log stacky curves: genus zero
- 8. Inductive presentation of the canonical ring
- 9. Log stacky base cases in genus 0
- 10. Spin canonical rings
- 11. Relative canonical algebras
- Appendix: Tables of canonical rings
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.- Dan Abramovich, Birational geometry for number theorists, Arithmetic geometry, Clay Math. Proc., vol. 8, Amer. Math. Soc., Providence, RI, 2009, pp. 335–373. MR 2498065
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