Lectures on K3 Surfaces

ISBN-13: 9781107153042 / Angielski / Twarda / 2016 / 496 str.

Daniel Huybrechts

Opis

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.

Recenzje

'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

Spis treści

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.