"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"--Provided by publisher.
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.
`This book fills a great need: it is almost the only place the foundations of the moduli theory of sheaves on algebraic varieties appear 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
`The authors have created a true masterpiece of mathematical exposition... This inspiring book belongs in the hands of any mathematician who has ever encountered a vector bundle on an algebraic variety.' Maxlieblich, University of Washington
Cambridge university Press has a long and honourable history of publishing in mathematics and counts many classics of the mathematical literature within its list. Some of these titles have been out of print for many years now and yet the methods which they espouse are still of considerable relevance today.
The Cambridge Mathematical Library will provide an inexpensive edition of these titles in a durable paperback format and at a price that will make the books attractive to individuals wishing to add them to their own personal libraries. It is intended that certain volumes in the series will have forewords, written by leading experts in the subject, which will place the title in its historical and mathematical context
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