The canonical ring of a stacky curve

The canonical ring of a stacky curve

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Détails bibliographiques
Auteurs principaux : Voight John (Auteur), Zureick-Brown David (Auteur)
Format : Livre
Langue : anglais
Titre complet : The canonical ring of a stacky curve / John Voight, David Zureick-Brown
Publié : Providence (R.I.) : American Mathematical Society , C 2022
Description matérielle : 1 vol. (V-144 p.)
Collection : Memoirs of the American Mathematical Society ; 1362
Sujets :
Courbes algébriques
Anneaux commutatifs
Documents associés : Autre format: The canonical ring of a stacky curve
  • 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 subjectivity
  • 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 Rieman 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 theorem: By order of stacky point
  • 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 Relatve stacky curves
  • 11.3 Modular forms and application to Rustom's conjecture
  • Appendix: Tables of canonical rings
  • Bibliography