Shigeyuki Kondō – författare

This book, consisting of two volumes, gives a contemporary account of the study of the class of projective algebraic surfaces known as Enriques surfaces. These surfaces were discovered more than 125 years by F. Enriques in an attempt to extend the characterization of rational algebraic curves to the case of algebraic surfaces. The novel feature of the present exposition is that no assumption on the characteristic of the ground field is assumed. This requirement calls for exploring the geometry of such surfaces by purely geometric and arithmetic methods that do not rely on transcendental methods such as the theory of periods of algebraic surfaces of type K3, which are close relatives of Enriques surfaces. Some of the methods use many technical tools from algebraic geometry that are discussed in Volume 1 and will be a useful source of reference for the study of algebraic surfaces over fields of positive characteristic. Volume 1 also contains a detailed exposition of the theory of elliptic surfaces over fields of arbitrary characteristic. The second volume discusses many new topics — for example, the theory of automorphisms of Enriques surfaces and the relationships with hyperbolic geometry. Together, the two volumes contain many examples and an extensive bibliography made up of more than 700 items.

This book, consisting of two volumes, gives a contemporary account of the study of the class of projective algebraic surfaces known as Enriques surfaces. These surfaces were discovered more than 125 years by F. Enriques in an attempt to extend the characterization of rational algebraic curves to the case of algebraic surfaces. The novel feature of the present exposition is that no assumption on the characteristic of the ground field is assumed. This requirement calls for exploring the geometry of such surfaces by purely geometric and arithmetic methods that do not rely on transcendental methods such as the theory of periods of algebraic surfaces of type K3, which are close relatives of Enriques surfaces. Some of the methods use many technical tools from algebraic geometry that are discussed in Volume 1 and will be a useful source of reference for the study of algebraic surfaces over fields of positive characteristic. Volume 1 also contains a detailed exposition of the theory of elliptic surfaces over fields of arbitrary characteristic. The second volume discusses many new topics — for example, the theory of automorphisms of Enriques surfaces and the relationships with hyperbolic geometry. Together, the two volumes contain many examples and an extensive bibliography made up of more than 700 items.

Contains the proceedings of the 6th Mathematical Society of Japan Seasonal Institute Development of Moduli Theory, which was held as the Seasonal Institute 2013, with support from the Mathematical Society of Japan and the 2013 Research Project of the Research Institute of Mathematical Science, Kyoto University. This volume consists of five survey articles and eight research articles.