"May 2022, volume 277, number 1362 (third of 6 numbers)." Includes bibliographical references (pages 139-144).
Contents:
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.
Series:
Memoirs of the American Mathematical Society, 0065-9266 ; Number 1362
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