Blowing up of non-commutative smooth surfaces / Michel Van den Bergh.

Format:

Book

Author/Creator:

Bergh, M. van den, author.

Series:

Memoirs of the American Mathematical Society ; no. 734.

Memoirs of the American Mathematical Society, 0065-9266 ; number 734

Language:

English

Subjects (All):

Noncommutative differential geometry.

Blowing up (Algebraic geometry).

Physical Description:

1 online resource (157 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2001.

Language Note:

English

Summary:

This book is intended for graduate students and research mathematicians interested in associative rings and algebras, and noncommutative geometry.

Contents:

""Contents""; ""Chapter 1. Introduction""; ""1.1. Motivation""; ""1.2. Construction""; ""1.3. General properties""; ""1.4. Non-commutative Del-Pezzo surfaces""; ""1.5. Exceptional simple objects""; ""1.6. Non-commutative cubic surfaces""; ""1.7. Acknowledgement""; ""Chapter 2. Preliminaries on category theory""; ""Chapter 3. Non-commutative geometry""; ""3.1. Bimodules""; ""3.2. Graded modules, bimodules and algebras""; ""3.3. Quotients of the identity functor""; ""3.4. Ideals in the identity functor""; ""3.5. Quasi-schemes""; ""3.6. Divisors""; ""3.7. Proj""

""3.8. Condition ""X"" and cohomological dimension""""3.9. Higher inverse images""; ""3.10. Algebras which are strongly graded modulo a Serre subcategory""; ""3.11. The positive part of certain graded algebras""; ""3.12. Veronese subalgebras""; ""Chapter 4. Pseudo-compact rings""; ""Chapter 5. Cohen-Macaulay curves embedded in quasi-schemes""; ""5.1. Preliminaries""; ""5.2. Some computations""; ""5.3. Completion of objects in mod(X)""; ""5.4. Completion of bimodules""; ""5.5. The category C[sub(f,p)]""; ""5.6. Completion of algebras""

""5.7. Multiplicities in the case that Ï? has infinite order""""Chapter 6. Blowing up a point on a commutative divisor""; ""6.1. Some ideals""; ""6.2. Some Rees algebras""; ""6.3. Definition of blowing up""; ""6.4. The normal bundle""; ""6.5. Birationality""; ""6.6. The exceptional curve""; ""6.7. The structure of the exceptional curve""; ""6.8. The strict transform""; ""6.9. A result on K[sub(0)] of some categories""; ""Chapter 7. Derived categories""; ""7.1. Generalities""; ""7.2. Admissible compositions of morphisms between quasi-schemes""

""Chapter 8. The derived category of a non-commutative blowup""""8.1. The formalism of semi-orthogonal decompositions""; ""8.2. Generalities""; ""8.3. Computation of some derived functors""; ""8.4. The main theorem""; ""Chapter 9. Some results on graded algebras and their sections""; ""9.1. Generalities""; ""9.2. The case of a blowing up""; ""Chapter 10. Quantum plane geometry""; ""10.1. Multiplicities of some objects""; ""10.2. Classification of lines and conics""; ""Chapter 11. Blowing up n points in an elliptic quantum plane""; ""11.1. Derived categories""

""11.2. Exceptional simple objects""""Chapter 12. Non-commutative cubic surfaces""; ""Appendix A. Two-categories""; ""Appendix B. Summary of notations""; ""Appendix C. Index of terminology""; ""Bibliography""

Notes:

"November 2001, volume 154, number 734 (end of volume)."

Includes bibliographical references (pages 139-140) and index.

Description based on print version record.

ISBN:

1-4704-0327-7