By Jean-Pierre Demailly

This quantity is a ramification of lectures given via the writer on the Park urban arithmetic Institute (Utah) in 2008, and on different events. the aim of this quantity is to explain analytic suggestions precious within the examine of questions concerning linear sequence, multiplier beliefs, and vanishing theorems for algebraic vector bundles. the writer goals to be concise in his exposition, assuming that the reader is already just a little familiar with the elemental options of sheaf concept, homological algebra, and intricate differential geometry. within the ultimate chapters, a few very fresh questions and open difficulties are addressed--such as effects relating to the finiteness of the canonical ring and the abundance conjecture, and effects describing the geometric constitution of Kahler kinds and their confident cones.

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