Noncommutative algebraic geometry

by Bellamy, Gwyn

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Title Statements

Full title :Noncommutative algebraic geometry / Gwyn Bellamy, University of Glasgow, Daniel Rogalski, University of California, San Diego, Travis Shedler, Imperial College London, J. Toby Stafford, University of Manchester, Michael Wemyss, Michael Wemyss.

Edition Statements

Publication Date:2016.

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:New York, NY
Language:eng
Publication Date:2016.

The Physical Object

Description:x, 356 pages : : illustrations ; : 25 cm.

Edition Identifiers

ISBN:9781107129542, 1107129540, 9781107570030, 1107570034
oclc:ocn947269847
LC Classification:QA564
Dewey Decimal:516.3/5

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 -- I…