Calabi-Yau Manifolds and Related Geometries

Lectures at a Summer School in Nordfjordeid, Norway, June 2001
Softcover Nachdruck of the original 1. Auflage 2003
ISBN: 978-3-540-44059-8
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 244 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 388 g

Reihe: Universitext

This is an introduction to a very active field of research, on the boundary between mathematics and physics. It is aimed at graduate students and researchers in geometry and string theory. Proofs or sketches are given for many important results.

From the reviews:

"An excellent introduction to current research in the geometry of Calabi-Yau manifolds, hyper-Kähler manifolds, exceptional holonomy and mirror symmetry.This is an excellent and useful book." --MATHEMATICAL REVIEWS

Zielgruppe

Research

Autoren/Hrsg.

Huybrechts, Daniel

Gross, Mark

Joyce, Dominic

Ellingsrud, Geir

Ranestad, Kristian

Olson, Loren

Stromme, Stein A.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

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.