Daniel Huybrechts

Lectures on K3 Surfaces (eBook, ePUB)

• Format: ePub

Produktbeschreibung

K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi-Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin-Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 26. September 2016
• Englisch
• ISBN-13: 9781316797013
• Artikelnr.: 52847741

Autorenporträt

Daniel Huybrechts is a professor at the Mathematical Institute of the University of Bonn. He previously held positions at the Université Denis Diderot Paris 7 and the University of Cologne. He is interested in algebraic geometry, particularly special geometries with rich algebraic, analytic, and arithmetic structures. His current work focuses on K3 surfaces and higher dimensional analogues. He has published four books.

Inhaltsangabe

Preface
1. Basic definitions
2. Linear systems
3. Hodge structures
4. Kuga-Satake construction
5. Moduli spaces of polarised K3 surfaces
6. Periods
7. Surjectivity of the period map and Global Torelli
8. Ample cone and Kähler cone
9. Vector bundles on K3 surfaces
10. Moduli spaces of sheaves on K3 surfaces
11. Elliptic K3 surfaces
12. Chow ring and Grothendieck group
13. Rational curves on K3 surfaces
14. Lattices
15. Automorphisms
16. Derived categories
17. Picard group
18. Brauer group.