Cover Image

Noncommutative algebraic geometry /

Bibliographic Details
Main Authors: Bellamy, Gwyn (Author), Rogalski, Daniel (Author), Schedler, Travis (Author), Stafford, J. Toby (Author), Wemyss, Michael (Author)
Format: Book
Language:English
Published: New York, NY : Cambridge University Press, 2016.
Series:Mathematical Sciences Research Institute publications ; 64.
Subjects:
Geometry, Algebraic.
Noncommutative algebras.
Géométrie algébrique.
Algèbres non commutatives.
Nichtkommutative Geometrie
Algebraische Geometrie
Table of Contents:
  • Ch. I Noncommutative projective geometry
  • Introduction
  • 1.Review of basic background and the Diamond Lemma
  • 2.Artin
  • Schelter regular algebras
  • 3.Point modules
  • 4.Noncommutative projective schemes
  • 5.Classification of noncommutative curves and surfaces
  • ch. II Deformations of algebras in noncommutative geometry
  • Introduction
  • 1.Motivating examples
  • 2.Formal deformation theory and Kontsevich's theorem
  • 3.Hochschild cohomology and infinitesimal deformations
  • 4.Dglas, the Maurer
  • Cartan formalism, and proof of formality theorems
  • 5.Calabi
  • Yau algebras and isolated hypersurface singularities
  • ch. III Symplectic reflection algebras
  • Introduction
  • 1.Symplectic reflection algebras
  • 2.Rational Cherednik algebras at t = 1
  • 3.The symmetric group
  • 4.The KZ functor
  • 5.Symplectic reflection algebras at t = 0
  • ch. IV Noncommutative resolutions
  • Introduction
  • Acknowledgments
  • 1.Motivation and first examples
  • 2.NCCRs and uniqueness issues
  • 3.From algebra to geometry: quiver GIT
  • 4.Into derived categories
  • 5.McKay and beyond
  • 6.Appendix: Quiver representations
  • Solutions to the exercises
  • I.Noncommutative projective geometry
  • II.Deformations of algebras in noncommutative geometry
  • III.Symplectic reflection algebras
  • IV.Noncommutative resolutions.