Noncommutative algebraic geometry / G.Bellamy et al. - Cambridge: Cambridge university press: MSRI, 2016. - x, 356 p.: ill. - (Mathematical sciences research institute publications / Mathematical sciences research institute (Berkeley); 64). - Bibliogr.: p.343-352. - Ind.: p.353-356. - ISBN 978-1-107-12954-2 Шифр: (И/В18-N76) 02  Место хранения:   02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents

Preface ....................................................... vii Introduction .................................................... 1 Chapter I. Noncommutative projective geometry .................. 13 Introduction ................................................... 13 1 Review of basic background and the Diamond Lemma ............ 14 2 Artin-Schelter regular algebras ............................. 30 3 Point modules ............................................... 42 4 Noncommutative projective schemes ........................... 51 5 Classification of noncommutative curves and surfaces ........ 62 Chapter II. Deformations of algebras in noncommutative geometry ....................................................... 71 Introduction ................................................... 71 1 Motivating examples ......................................... 75 2 Formal deformation theory and Kontsevich's theorem ......... 104 3 Hochschild cohomology and infinitesimal deformations ....... 124 4 Dglas, the Maurer-Cartan formalism, and proof of formality theorems ......................................... 136 5 Calabi-Yau algebras and isolated hypersurface singularities .............................................. 157 Chapter III. Symplectic reflection algebras ................... 167 Introduction .................................................. 167 1 Symplectic reflection algebras ............................. 171 2 Rational Cherednik algebras at t = 1 ....................... 184 3 The symmetric group ........................................ 197 4 The KZ functor ............................................. 211 5 Symplectic reflection algebras at t = 0 .................... 224 Chapter IV Noncommutative resolutions ........................ 239 Introduction .................................................. 239 Acknowledgments ............................................... 240 1 Motivation and first examples .............................. 240 2 NCCRs and uniqueness issues ................................ 250 3 From algebra to geometry: quiver GIT ....................... 261 4 Into derived categories .................................... 270 5 McKay and beyond ........................................... 285 6 Appendix: Quiver representations ........................... 297 Solutions to the exercises .................................... 307 I Noncommutative projective geometry ........................ 307 II Deformations of algebras in noncommutative geometry ....... 316 III Symplectic reflection algebras ............................ 332 IV Noncommutative resolutions ................................ 337 Bibliography .................................................. 343 Index ......................................................... 353