Hyperbolicity properties of algebraic varieties

Since its introduction in the 70's, the notion of Kobayashi hyperbolicity has attracted a lot of attention in the mathematical community. Besides its aspects exclusively belonging to the several complex variables world, an extremely fascinating theme is that of its interactions with the algebraic, arithmetic, and differential geometric properties of algebraic varieties. These interactions are essentially what this book is about.

Some of the issues addressed are : distribution and distribution of values of entire curves, algebraic analogues of hyperbolicity, hyperbolicity properties of projective hypersurfaces and of varieties of general type, hyperbolicity of moduli spaces, relationships between hyperbolicity and negative curvature, distribution of rational points on hyperbolic (arithmetic) varieties, and interplay of different kinds of natural fibrations on algebraic varieties and hyperbolicity.

The volume has the ambition to make a point of the state of the art, each chapter treating a different aspect of the subject, trying to keep the language friendly enough to encourage in particular PhD students as well as young researchers in complex geometry to get into the most recent advances in the study of hyperbolicity properties of algebraic varieties.