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.
Reihe
Auflage
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Upper undergraduate
Maße
Höhe: 229 mm
Breite: 162 mm
Gewicht
ISBN-13
978-3-528-06907-0 (9783528069070)
DOI
10.1007/978-3-663-11624-0
Schweitzer Klassifikation
Dr. Huybrechts forscht an der Humboldt Universität Berlin und Dr. Lehn an der Universität Bielefeld.
Introduction - Preliminaries - Families of Sheaves - The Grauert-Mülich Theorem - Moduli Spaces - Construction Methods - Moduli Spaces on K3 Surfaces - Restriction of Sheaves to Curves - Line Bundles on the Moduli Space - Irreducibility and Smoothness - Symplectic Structures - Birational Properties
