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[null,"1.","Record Nr.",null,"UNINA9910971643803321"]
[null,null,"Autore",null,"Voight John"]
[null,null,"Titolo",null,"The Canonical Ring of a Stacky Curve"]
[null,null,"Pubbl/distr/stampa",null,"Providence : , : American Mathematical Society, , 2022"]
[{"$nulls":4},"©2022"]
[null,null,"ISBN",null,"9781470470944"]
[{"$nulls":4},"1470470942"]
[null,null,"Edizione",null,"[1st ed.]"]
[null,null,"Descrizione fisica",null,"1 online resource (156 pages)"]
[null,null,"Collana",null,"Memoirs of the American Mathematical Society ; ; v.277"]
[null,null,"Classificazione",null,"14Q0511F11"]
[null,null,"Disciplina",null,"516.3/52"]
[{"$nulls":4},"516.352"]
[null,null,"Soggetti",null,"Curves, Algebraic"]
[{"$nulls":4},"Algebraic geometry -- Computational aspects in algebraic geometry -- Curves"]
[{"$nulls":4},"Number theory -- Discontinuous groups and automorphic forms -- Holomorphic modular forms of integral weight"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"Cover -- Title page -- Chapter 1. Introduction -- 1.1. Motivation: Petri's theorem -- 1.2. Orbifold canonical rings -- 1.3. Rings of modular forms -- 1.4. Main result -- 1.5. Extensions and discussion -- 1.6. Previous work on canonical rings of fractional divisors -- 1.7. Computational applications -- 1.8. Generalizations -- 1.9. Organization and description of proof -- 1.10. Acknowledgements -- Chapter 2. Canonical rings of curves -- 2.1. Setup -- 2.2. Terminology -- 2.3. Low genus -- 2.4. Basepoint-free pencil trick -- 2.5. Pointed gin: High genus and nonhyperelliptic -- 2.6. Gin and pointed gin: Rational normal curve -- 2.7. Pointed gin: Hyperelliptic -- 2.8. Gin: Nonhyperelliptic and hyperelliptic -- 2.9. Summary -- Chapter 3. A generalized Max Noether's theorem for curves -- 3.1. Max Noether's theorem in genus at most 1 -- 3.2. Generalized Max Noether's theorem (GMNT) -- 3.3. Failure of surjectivity -- 3.4. GMNT: Nonhyperelliptic curves -- 3.5. GMNT: Hyperelliptic curves -- Chapter 4. Canonical rings of classical log curves -- 4.1. Main result: Classical log curves -- 4.2. Log curves: Genus 0 -- 4.3. Log curves: Genus 1 -- 4.4. Log degree 1: Hyperelliptic -- 4.5. Log degree 1: Nonhyperelliptic -- 4.6. Exceptional log cases -- 4.7. Log degree 2 -- 4.8. General log degree -- 4.9. Summary -- Chapter 5. Stacky curves -- 5.1. Stacky points -- 5.2. "]
[{"$nulls":4},"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."]
[{"$nulls":4},"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."]
[null,null,null,"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\"--"]