Derived Categories in Algebraic Geometry
Tokyo 2011
Seiten
2013
|
1., Aufl.
EMS Press (Verlag)
978-3-03719-115-6 (ISBN)
EMS Press (Verlag)
978-3-03719-115-6 (ISBN)
The study of derived categories is a subject that attracts increasingly many young mathematicians from various fields of mathematics, including abstract algebra, algebraic geometry, representation theory and mathematical physics.
The concept of the derived category of sheaves was invented by Grothendieck and Verdier in the 1960s as a tool to express important results in algebraic geometry such as the duality theorem. In the 1970s, Beilinson, Gelfand and Gelfand discovered that a derived category of an algebraic variety may be equivalent to that of a finite dimensional non-commutative algebra, and Mukai found that there are non-isomorphic algebraic varieties that have equivalent derived categories. In this way the derived category provides a new concept that has many incarnations. In the 1990s, Bondal and Orlov uncovered an unexpected parallelism between derived categories and birational geometry. Kontsevich’s homological mirror symmetry provided further motivation for the study of derived categories.
This book is the proceedings of a conference held at the University of Tokyo in January 2011 on the current status of the research on derived categories related to algebraic geometry. Most articles are survey papers on this rapidly developing field. The book is suitable for young mathematicians who want to enter this exciting field. Some basic knowledge of algebraic geometry is assumed.
The concept of the derived category of sheaves was invented by Grothendieck and Verdier in the 1960s as a tool to express important results in algebraic geometry such as the duality theorem. In the 1970s, Beilinson, Gelfand and Gelfand discovered that a derived category of an algebraic variety may be equivalent to that of a finite dimensional non-commutative algebra, and Mukai found that there are non-isomorphic algebraic varieties that have equivalent derived categories. In this way the derived category provides a new concept that has many incarnations. In the 1990s, Bondal and Orlov uncovered an unexpected parallelism between derived categories and birational geometry. Kontsevich’s homological mirror symmetry provided further motivation for the study of derived categories.
This book is the proceedings of a conference held at the University of Tokyo in January 2011 on the current status of the research on derived categories related to algebraic geometry. Most articles are survey papers on this rapidly developing field. The book is suitable for young mathematicians who want to enter this exciting field. Some basic knowledge of algebraic geometry is assumed.
| Erscheint lt. Verlag | 7.1.2013 |
|---|---|
| Reihe/Serie | EMS Series of Congress Reports |
| Verlagsort | Zürich |
| Sprache | englisch |
| Maße | 170 x 240 mm |
| Gewicht | 750 g |
| Einbandart | gebunden |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | abelian variety, non-commutative algebraic geometry, mirror symmetry, Donaldson-Thomas theory • Algebraic variety, derived category, triangulated category, Fourier-Mukai transform, cluster algebra • birational geometry, semi-orthogonal decomposition, exceptional collection, minimal model, flop, McKay correspondence, categorical action • birational geometry, semi-orthogonal decomposition, exceptional collection, minimal model, flop, McKay correspondence, categorical action |
| ISBN-10 | 3-03719-115-5 / 3037191155 |
| ISBN-13 | 978-3-03719-115-6 / 9783037191156 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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