Lectures on K3 Surfaces
ΡΠ΅Π½Ρ. 2016β―Π³. Β· Cambridge Studies in Advanced Mathematics ΠΠ½ΠΈΠ³Π°Β 158 Β· Cambridge University Press
ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½Π°Ρ ΠΊΠ½ΠΈΠ³Π°
499
ΠΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΡΡΡΠ°Π½ΠΈΡ
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ΠΠ± ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎΠΉ ΠΊΠ½ΠΈΠ³Π΅
K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of CalabiβYau 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 ArtinβTate, 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.
ΠΠ± Π°Π²ΡΠΎΡΠ΅
Daniel Huybrechts is a professor at the Mathematical Institute of the University of Bonn. He previously held positions at the UniversitΓ© 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.
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