Fourier-Mukai Transforms in Algebraic Geometry

Erscheinungsjahr 2006
ISBN: 978-0-19-929686-6
Verlag: OUP Oxford

Buch, Englisch, 280 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 640 g

This seminal text on Fourier-Mukai Transforms in Algebraic Geometry by a leading researcher and expositor is based on a course given at the Institut de Mathematiques de Jussieu in 2004 and 2005. Aimed at postgraduate students with a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. Including notions from other areas, e.g. singular cohomology, Hodge theory, abelian varieties, K3 surfaces; full proofs are given and exercises aid the reader throughout.

Autoren/Hrsg.

Huybrechts, D.

Huybrechts, Daniel

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Populärwissenschaftliche Werke
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

- Preface

- 1: Triangulated categories

- 2: Derived categories: a quick tour

- 3: Derived categories of coherent sheaves

- 4: Derived category and canonical bundle I

- 5: Fourier-Mukai transforms

- 6: Derived category and canonical bundle II

- 7: Equivalence criteria for Fourier-Mukai transforms

- 8: Spherical and exceptional objects

- 9: Abelian varieties

- 10: K3 surfaces

- 11: Flips and flops

- 12: Derived categories of surfaces

- 13: Where to go from here

- References

- Index

Über Autor(innen)

Daniel Huybrechts completed his Ph.D. in 1992 at the Universität Berlin. He is now a professor at the Institut de Mathématiques de Jussieu, Université Paris VII.