Lectures on K3 Surfaces

Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.

Daniel Huybrechts (Author)

9781107153042, Cambridge University Press

Hardback, published 26 September 2016

496 pages, 21 b/w illus.
23.4 x 15.7 x 3.2 cm, 0.82 kg

'The book is a welcome addition to the literature, especially since its scope ranges from a very good introduction to K3 surfaces to the more recent advances on these surfaces and related topics.' Felipe Zaldivar, MAA Reviews

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.

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.

Subject Areas: Mathematical physics [PHU], Topology [PBP], Geometry [PBM]