LEADER 05047nam 22005653 450 001 9910971643803321 005 20231110213248.0 010 $a9781470470944 010 $a1470470942 035 $a(CKB)5600000000455014 035 $a(MiAaPQ)EBC29731891 035 $a(Au-PeEL)EBL29731891 035 $a(OCoLC)1343249233 035 $a(EXLCZ)995600000000455014 100 $a20221021d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Canonical Ring of a Stacky Curve 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2022. 210 4$d©2022. 215 $a1 online resource (156 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.277 311 08$a9781470452285 311 08$a1470452286 327 $aCover -- 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. 327 $aChapter 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. 330 $a"Generalizing the classical theorems of Max Noether and Petri, we describe generators and relations for the canonical ring of a stacky curve, including an explicit Grobner basis. We work in a general algebro-geometric context and treat log canonical and spin canonical rings as well. As an application, we give an explicit presentation for graded rings of modular forms arising from finite-area quotients of the upper half-plane by Fuchsian groups"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aCurves, Algebraic 606 $aAlgebraic geometry -- Computational aspects in algebraic geometry -- Curves$2msc 606 $aNumber theory -- Discontinuous groups and automorphic forms -- Holomorphic modular forms of integral weight$2msc 615 0$aCurves, Algebraic. 615 7$aAlgebraic geometry -- Computational aspects in algebraic geometry -- Curves. 615 7$aNumber theory -- Discontinuous groups and automorphic forms -- Holomorphic modular forms of integral weight. 676 $a516.3/52 676 $a516.352 686 $a14Q05$a11F11$2msc 700 $aVoight$b John$01214654 701 $aZureick-Brown$b David$01800548 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910971643803321 996 $aThe Canonical Ring of a Stacky Curve$94345378 997 $aUNINA