The Geometry of Moduli Spaces of Sheaves

This highly regarded book is back in print and now updated to reflect recent advances in the field.

Daniel Huybrechts (Author), Manfred Lehn (Author)

9780521134200, Cambridge University Press

Paperback, published 27 May 2010

344 pages
22.4 x 15 x 2 cm, 0.48 kg

'Serving as a perfect introduction for beginners in the field, an excellent guide to the forefront of research in various directions, a valuable reference for active researchers, and as an abundant source of inspiration for mathematicians and physicists likewise, this book will certainly maintain both its particular significance and its indispensability for further generations of researchers in the field of algebraic sheaves (or vector bundles) and their moduli spaces.' Zentralblatt MATH

Now back in print, this highly regarded book has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces, which include moduli spaces in positive characteristic, moduli spaces of principal bundles and of complexes, Hilbert schemes of points on surfaces, derived categories of coherent sheaves, and moduli spaces of sheaves on Calabi–Yau threefolds. The authors review changes in the field since the publication of the original edition in 1997 and point the reader towards further literature. References have been brought up to date and errors removed. Developed from the authors' lectures, this book is ideal as a text for graduate students as well as a valuable resource for any mathematician with a background in algebraic geometry who wants to learn more about Grothendieck's approach.

Preface to the second edition
Preface to the first edition
Introduction
Part I. General Theory: 1. Preliminaries
2. Families of sheaves
3. The Grauert–Müllich Theorem
4. Moduli spaces
Part II. Sheaves on Surfaces: 5. Construction methods
6. Moduli spaces on K3 surfaces
7. Restriction of sheaves to curves
8. Line bundles on the moduli space
9. Irreducibility and smoothness
10. Symplectic structures
11. Birational properties
Glossary of notations
References
Index.

Subject Areas: Algebraic geometry [PBMW]