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Graded Syzygies / by Irena Peeva
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Algebra and Applications ; 14 | SpringerLink BücherPublisher: London : Springer-Verlag London Limited, 2011Description: Online-Ressource (XI, 302p. 23 illus, digital)ISBN:- 9780857291776
- 128297369X
- 9781282973695
- 515.733
- 512.44
- QA251.3
- QA247
Contents:
Summary: Graded Free Resolutions -- Hilbert Functions -- Monomial Resolutions -- Syzygies of Toric Ideals.Summary: The study of free resolutions is a core and beautiful area in Commutative Algebra. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given in order to illustrate ideas and key concepts. A valuable feature of the book is the inclusion of open problems and conjectures; these provide a glimpse of exciting, and often challenging, research directions in the field. Three types of problems are presented: Conjectures, Problems, and Open-Ended Problems. The latter do not describe specific problems but point to interesting directions for exploration. The first part of the monograph contains basic background material on graded free resolutions. Further coverage of topics includes syzygies over a polynomial ring, resolutions over quotient rings, lex ideals and Hilbert functions, compression, resolutions of monomial ideals, and syzygies of toric ideals. With a clear and self-contained exposition this text is intended for advanced graduate students and postdoctorates; it will be also of interest to senior mathematicians.PPN: PPN: 1650616392Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
CONTENTS; 1. Gradedpolynomialrings; Contents; Notation; 2. Gradedmodulesandhomomorphisms; 3. Gradedcomplexes; 4. Freeresolutions; 5. Resolving,thatis,RepeatedlySolving; 6. Homotopy; 7. Minimalfreeresolutions; 8. Encodingthestructureofamodule; 9. ProofofTheorem7.5(2); 10. Syzygies; 11. Bettinumbers; 12. GradedBettinumbers; 13. Theconnectinghomomorphism; 14. TheKoszulcomplex; 15. Finiteprojectivedimension; 16. Hilbertfunctions; 17. Pureresolutions; 18. Regularity; 19. Truncation; 20. Regularelements; 21. Polarization; 22. Deformations from Gröbnerbasistheory; 23. Computingagradedfreeresolution
24. Shortresolutions25 Cohen-MacaulayandGorensteinideals; 26. MultigradingsandTaylor'sresolution; 27. Mappingcones; 28. TheEliahou-Kervaireresolution; 29. ApplicationsofEliahou-Kervaire'sresolution; 30. Doublecomplexes; 31. DGalgebras; 32. Tworesolutions; 33. Betti numbers of infinite free resolutions; 34. Koszulrings; 35. Rate; 36. Topologicaltools; 37. Appendix:Toolsfromhomologicalalgebra; 38. Appendix:TorandExt; 39. Appendix: Gröbnerbasis; 40. Notation; 41. Lexideals; 42. Compression; 43. Multicompression; 44. Green'sTheorem; 45. ProofsofMacaulay'sTheorem; 46. Compressionideals
47. IdealswithafixedHilbertfunction48. Gotzmann'sPersistenceTheorem; 49. Numericalversions; 50. Hilbertfunctionsoverquotientrings; 51. Squarefreeidealsplussquares; 52. Clements-Lindströmrings; 53. The Eisenbud-Green-Harris Conjecture; 54. ExamplesandNotation; 55. Homogenizationanddehomogenization; 56. Subresolutions; 57. Simplicialandcellularresolutions; 58. Thelcm-lattice; 59. TheScarfcomplex; 60. Rootings and Lyubeznik's resolution; 61. Betti numbers via simplicial complexes; 62. TheStanley-Reisnercorrespondence; 63. Quadraticmonomialideals; 64. Infinite free monomial resolutions
65. BasicsandNotation66. Examples; 67. Betti numbers via simplicial complexes; 68. Projectivedimension; 69. TheScarfcomplex; 70. Generictoricideals; 71. TheLawrencelifting; 72. Hilbertfunctions; 73. Infinite free resolutions; 74. Koszultoricrings; References; Index;
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