Geometry of Moduli Spaces of Sheaves

This volume is intended to serve as an introduction to the theory of semistable sheaves and at the same time to provide a survey of research results on the geometry of moduli spaces. It introduces the basic concepts of the theory: Hilbert polynomial, slope, stability, Harder-Narasimhan filtration and Grothendieck's Quot-scheme. The book presents detailed proofs of the Grauert-Mulich Theorem, the Bogomolov Inequality, the semistability of tensor products and the boundedness of the family of semistable sheaves.
 
This volume is intended to serve as an introduction to the theory of semistable sheaves and at the same time to provide a survey of research results on the geometry of moduli spaces. It introduces the basic concepts of the theory: Hilbert polynomial, slope, stability, Harder-Narasimhan filtration and Grothendieck's Quot-scheme. The book presents detailed proofs of the Grauert-Mulich Theorem, the Bogomolov Inequality, the semistability of tensor products and the boundedness of the family of semistable sheaves.