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The Geometry of Moduli Spaces of Sheaves


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Table of Contents

Preface to the second edition; Preface to the first edition; Introduction; Part I. General Theory: 1. Preliminaries; 2. Families of sheaves; 3. The Grauert-Mullich 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.

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

About the Author

Daniel Huybrechts is Professor in the Mathematical Institute at the University of Bonn. Manfred Lehn is Professor in the Mathematical Institute at Johannes Gutenberg University, Mainz, Germany.


'The authors have created a true masterpiece of mathematical exposition. Bringing together disparate ideas developed gradually over the last fifty years into a cohesive whole, Huybrechts and Lehn provide a compelling and comprehensive view of an essential topic in algebraic geometry. The new edition is full of gems that have been discovered since the first edition. This inspiring book belongs in the hands of any mathematician who has ever encountered a vector bundle on an algebraic variety.' Max Lieblich, University of Washington
'This book fills a great need: it is almost the only place the foundations of the moduli theory of sheaves on algebraic varieties appears in any kind of expository form. The material is of basic importance to many further developments: Donaldson-Thomas theory, mirror symmetry, and the study of derived categories.' Rahul Pandharipande, Princeton University
'This is a wonderful book; it's about time it was available again. It is the definitive reference for the important topics of vector bundles, coherent sheaves, moduli spaces and geometric invariant theory; perfect as both an introduction to these subjects for beginners, and as a reference book for experts. Thorough but concise, well written and accurate, it is already a minor modern classic. The new edition brings the presentation up to date with discussions of more recent developments in the area.' Richard Thomas, Imperial College London
'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

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