Noncommutative algebraic geometry (Cambridge, 2016). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаNoncommutative 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
 

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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

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