The Geometry of Moduli Spaces of Sheaves [Paperback]

This highly regarded book is back in print and now updated to reflect recent advances in the field.This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.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 CalabiYau 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 GrauertM?llich 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;lӕ