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