The Canonical Ring of a Stacky Curve.

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
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