Lectures on K3 Surfaces

K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of CalabiYau 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 ArtinTate 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.