Analytic Methods In Algebraic Geometry Jeanpierre Demailly by Jean-pierre Demailly 9787040305319, 7040305313 instant download after payment.

This volume is an expansion of lectures given by the author at the Park City Mathematics Institute in 2008 as well as in other places. The main purpose of the book is to describe analytic techniques which are useful to study questions such as linear series, multiplier ideals and vanishing theorems for algebraic vector bundles. The exposition tries to be as condensed as possible, assuming that the reader is already somewhat acquainted with the basic concepts pertaining to sheaf theory, homological algebra and complex differential geometry. In the final chapters, some very recent questions and open problems are addressed, for example results related to the finiteness of the canonical ring and the abundance conjecture, as well as results describing the geometric structure of Kahler varieties and their positive cones.