The Geometry of Moduli Spaces of Sheaves: A Publication of the Max-Planck-Institut für Mathematik, Bonn (Aspects of Mathematics) (German Edition) - Hardcover

Huybrechts, Daniel; Lehn, Manfred

Hardcover

ISBN 10: 3528069074 ISBN 13: 9783528069070

Publisher: Vieweg+Teubner Verlag, 1997

Synopsis

This book is intended to serve as an introduction to the theory of semistable sheaves and at the same time to provide a survey of recent research results on the geometry of moduli spaces.
The first part introduces the basic concepts in the theory: Hilbert polynomial, slope, stability, Harder-Narasimhan filtration, Grothendieck's Quot-scheme. It presents detailed proofs of the Grauert-Mülich Theorem, the Bogomolov Inequality, the semistability of tensor products, and the boundedness of the family of semistable sheaves. It also gives a self-contained account of the construction of moduli spaces of semistable sheaves on a projective variety à la Gieseker, Maruyama, and Simpson.
The second part presents some of the recent results of the geometry of moduli spaces of sheaves on an algebraic surface, following work of Mukai, O'Grady, Gieseker, Li and many others. In particular, moduli spaces of sheaves on K3 surfaces and determinant line bundles on the moduli spaces are treated in some detail. Other topics include the Serre correspondence, restriction of stable bundles to curves, symplectic structures, irreducibility and Kodaira-dimension of moduli spaces.

About this title

About the Author

Dr. Huybrechts forscht an der Humboldt Universität Berlin und Dr. Lehn an der Universität Bielefeld.

Edition details

• Publisher: Vieweg+Teubner Verlag
• Publication date: 1997
• Language: German
• ISBN 10: 3528069074
• ISBN 13: 9783528069070
• Binding: Hardcover
• Number of pages: 270