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AuthorGross, Mark. author
TitleCalabi-Yau Manifolds and Related Geometries [electronic resource] : Lectures at a Summer School in Nordfjordeid, Norway, June 2001 / by Mark Gross, Dominic Joyce, Daniel Huybrechts ; edited by Geir Ellingsrud, Kristian Ranestad, Loren Olson, Stein A. Strรธmme
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003
Connect tohttp://dx.doi.org/10.1007/978-3-642-19004-9
Descript VIII, 244 p. 2 illus. online resource

CONTENT

I. Riemannian Holonomy Groups and Calibrated Geometry -- 1 Introduction -- 2 Introduction to Holonomy Groups -- 3 Bergerโ{128}{153}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 Hyperkรคhler Manifolds -- 20 Introduction -- 21 Holomorphic Symplectic Manifolds -- 22 Deformations of Complex Structures -- 23 The Beauville-Bogomolov Form -- 24 Cohomology of Compact Hyperkรคhler Manifolds -- 25 Twistor Space and Moduli Space -- 26 Projectivity of Hyperkรคhler Manifolds -- 27 Birational Hyperkรคhler Manifolds -- 18 The (Birational) Kahler Cone -- References


Mathematics Algebraic geometry Differential geometry Topology Mathematics Differential Geometry Algebraic Geometry Topology



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