K3 surfaces

Shigeyuki Kondō

K3 surfaces are a key piece in the classification of complex analytic or algebraic surfaces. The term was coined by A. Weil in 1958 - a result of the initials Kummer, Kähler, Kodaira, and the mountain K2 found in Karakoram. The most famous example is the Kummer surface discovered in the 19th century.K3 surfaces can be considered as a 2-dimensional analogue of an elliptic curve, and the theory of periods - called the Torelli-type theorem for K3 surfaces - was established around 1970. Since then, several pieces of research on K3 surfaces have been undertaken and more recently K3 surfaces have even become of interest in theoretical physics.The main purpose of this book is an introduction to the Torelli-type theorem for complex analytic K3 surfaces, and its applications. The theory of lattices and their reflection groups is necessary to study K3 surfaces, and this book introduces these...