Hodge theory and complex algebraic geometry, I / Claire Voisin ; translated by Leila Schneps

This book is the first volume of a modern introduction to transcendental algebraic geometry, with a special emphasis on the underlying aspects of Kählerian geometry and Hodge theory. Accordingly, this first volume focuses on the merely complex-analytic foundations of the subject without particularly mentioning complex projective manifolds, whilst the forthcoming second volume will be devoted to the systematic application of the analytic framework in different algebro-geometric directions relating Hodge theory, topology and the study of algebraic cycles on smooth projective manifolds. The ultimate goal of the text, as a whole, is to provide a comprehensive, self-contained and up-to-date account of Hodge theory and the theory of algebraic cycles as developed, during the past thirty years, by P. Griffiths and his school, P. Deligne, S. Bloch, and many others.

With regard to this program and its methodical realization, the present first volume is perfectly suitable for seasoned students either as a profound general introduction to the analytic foundations of complex algebraic geometry, or as an excellent preparation for the second volume, which apparently will lead them to the forefront of contemporary research in complex algebraic geometry. (Zentralblatt)

Bibliogr. p. 315-318. Index