Description: 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 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]
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BIC Subject Area 1: Mathematical physics [PHU]
BIC Subject Area 2: Topology [PBP]
BIC Subject Area 3: Geometry [PBM]
Number of Pages: 496 Pages
Language: English
Publication Name: Lectures on K3 Surfaces
Publisher: Cambridge University Press
Publication Year: 2016
Subject: Mathematics, Physics
Item Height: 234 mm
Item Weight: 820 g
Type: Textbook
Author: Daniel Huybrechts
Series: Cambridge Studies in Advanced Mathematics
Item Width: 157 mm
Format: Hardcover
