| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910971643803321 |
|
|
Autore |
Voight John |
|
|
Titolo |
The Canonical Ring of a Stacky Curve |
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Providence : , : American Mathematical Society, , 2022 |
|
©2022 |
|
|
|
|
|
|
|
|
|
ISBN |
|
|
|
|
|
|
|
|
Edizione |
[1st ed.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (156 pages) |
|
|
|
|
|
|
Collana |
|
Memoirs of the American Mathematical Society ; ; v.277 |
|
|
|
|
|
|
Classificazione |
|
|
|
|
|
|
Altri autori (Persone) |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
|
|
Soggetti |
|
Curves, Algebraic |
Algebraic geometry -- Computational aspects in algebraic geometry -- Curves |
Number theory -- Discontinuous groups and automorphic forms -- Holomorphic modular forms of integral weight |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
Nota di contenuto |
|
Cover -- Title page -- Chapter 1. Introduction -- 1.1. Motivation: Petri's theorem -- 1.2. Orbifold canonical rings -- 1.3. Rings of modular forms -- 1.4. Main result -- 1.5. Extensions and discussion -- 1.6. Previous work on canonical rings of fractional divisors -- 1.7. Computational applications -- 1.8. Generalizations -- 1.9. Organization and description of proof -- 1.10. Acknowledgements -- Chapter 2. Canonical rings of curves -- 2.1. Setup -- 2.2. Terminology -- 2.3. Low genus -- 2.4. Basepoint-free pencil trick -- 2.5. Pointed gin: High genus and nonhyperelliptic -- 2.6. Gin and pointed gin: Rational normal curve -- 2.7. Pointed gin: Hyperelliptic -- 2.8. Gin: Nonhyperelliptic and hyperelliptic -- 2.9. Summary -- Chapter 3. A generalized Max Noether's theorem for curves -- 3.1. Max Noether's theorem in genus at most 1 -- 3.2. Generalized Max Noether's theorem (GMNT) -- 3.3. Failure of surjectivity -- 3.4. GMNT: Nonhyperelliptic curves -- 3.5. GMNT: Hyperelliptic curves -- Chapter 4. Canonical rings of classical log curves -- 4.1. Main result: Classical log curves -- 4.2. Log curves: Genus 0 -- 4.3. Log curves: Genus 1 -- 4.4. Log degree 1: |
|
|
|
|
|
|
|
|
|
|
|
Hyperelliptic -- 4.5. Log degree 1: Nonhyperelliptic -- 4.6. Exceptional log cases -- 4.7. Log degree 2 -- 4.8. General log degree -- 4.9. Summary -- Chapter 5. Stacky curves -- 5.1. Stacky points -- 5.2. Definition of stacky curves -- 5.3. Coarse space -- 5.4. Divisors and line bundles on a stacky curve -- 5.5. Differentials on a stacky curve -- 5.6. Canonical ring of a (log) stacky curve -- 5.7. Examples of canonical rings of log stacky curves -- Chapter 6. Rings of modular forms -- 6.1. Orbifolds and stacky Riemann existence -- 6.2. Modular forms -- Chapter 7. Canonical rings of log stacky curves: genus zero -- 7.1. Toric presentation -- 7.2. Effective degrees -- 7.3. Simplification. |
Chapter 8. Inductive presentation of the canonical ring -- 8.1. The block term order -- 8.2. Block term order: Examples -- 8.3. Inductive theorem: large degree canonical divisor -- 8.4. Main theorem -- 8.5. Inductive theorems: Genus zero, 2-saturated -- 8.6. Inductive theorem: By order of stacky point -- 8.7. Poincaré generating polynomials -- Chapter 9. Log stacky base cases in genus 0 -- 9.1. Beginning with small signatures -- 9.2. Canonical rings for small signatures -- 9.3. Conclusion -- Chapter 10. Spin canonical rings -- 10.1. Classical case -- 10.2. Modular forms -- 10.3. Genus zero -- 10.4. Higher genus -- Chapter 11. Relative canonical algebras -- 11.1. Classical case -- 11.2. Relative stacky curves -- 11.3. Modular forms and application to Rustom's conjecture -- Appendix: Tables of canonical rings -- Bibliography -- Back Cover. |
|
|
|
|
|
|
Sommario/riassunto |
|
"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 Grobner 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"-- |
|
|
|
|
|
|
|
| |