- Publisher: Cambridge University Press
- Online publication date: October 2016
- Print publication year: 2016
- Online ISBN: 9781316594193
- Book DOI: https://doi.org/10.1017/CBO9781316594193
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.
Rob Lazarsfeld - State University of New York, Stony Brook
Klaus Hulek - Leibniz Universität Hannover
Kieran G. O'Grady - Università degli Studi di Roma ‘La Sapienza', Italy
Arnaud Beauville - Université de Nice, Sophia Antipolis
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