Calabi-Yau Manifolds and Related Geometries

Lectures at a Summer School in Nordfjordeid, Norway, June 2001

von Dominic Joyce, Daniel Huybrechts, Mark Gross

252 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

I. Riemannian Holonomy Groups and Calibrated Geometry.- 1 Introduction.- 2 Introduction to Holonomy Groups.- 3 Berger's Classification of Holonomy Groups.- 4 Kahler Geometry and Holonomy.- 5 The Calabi Conjecture.- 6 The Exceptional Holonomy Groups.- 7 Introduction to Calibrated Geometry.- 8 Calibrated Submanifolds in ?n.- 9 Constructions of SL m-folds in ?m.- 10 Compact Calibrated Submanifolds.- 11 Singularities of Special Lagrangian m-folds.- 12 The SYZ Conjecture, and SL Fibrations.- II. Calabi-Yau Manifolds and Mirror Symmetry.- 13 Introduction.- 14 The Classical Geometry of Calabi-Yau Manifolds.- 15 Kahler Moduli and Gromov-Witten Invariants.- 16 Variation and Degeneration of Hodge Structures.- 17 A Mirror Conjecture.- 18 Mirror Symmetry in Practice.- 19 The Strominger-Yau-Zaslow Approach to Mirror Symmetry.- III. Compact Hyperkähler Manifolds.- 20 Introduction.- 21 Holomorphic Symplectic Manifolds.- 22 Deformations of Complex Structures.- 23 The Beauville-Bogomolov Form.- 24 Cohomology of Compact Hyperkähler Manifolds.- 25 Twistor Space and Moduli Space.- 26 Projectivity of Hyperkähler Manifolds.- 27 Birational Hyperkähler Manifolds.- 18 The (Birational) Kahler Cone.- References.

• Reihe: Universitext
• Themen: Mathematik und Naturwissenschaften Mathematik Topologie
• ISBN: 9783540440598
• Sprache: Englisch
• Erscheinungsdatum: 27.11.2002
• Größe: 235 x 155 mm
• Verlag: Springer
• Herausgegeben von: Kristian Ranestad, Geir Ellingsrud, Loren Olson, Stein A. Stromme