Lectures on K3 Surfaces

Inbunden, Engelska, 2016

Del 158 i serien Cambridge Studies in Advanced Mathematics

837 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2016-09-26
Mått:157 x 234 x 32 mm
Vikt:820 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Studies in Advanced Mathematics
Antal sidor:496
Förlag:Cambridge University Press
ISBN:9781107153042

Utforska kategorier

Topologi inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Mer om författaren

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.

Recensioner i media

'K3 surfaces play something of a magical role in algebraic geometry and neighboring areas. They arise in astonishingly varied contexts, and the study of K3 surfaces has propelled the development of many of the most powerful tools in the field. The present lectures provide a comprehensive and wide-ranging survey of this fascinating subject. Suitable both for study and as a reference work, and written with Huybrechts's usual clarity of exposition, this book is destined to become the standard text on K3 surfaces.' Rob Lazarsfeld, State University of New York, Stony Brook

Innehållsförteckning

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.