By Jean-Pierre Demailly

This quantity is a diffusion of lectures given by way of the writer on the Park urban arithmetic Institute (Utah) in 2008, and on different events. the aim of this quantity is to explain analytic innovations beneficial within the learn of questions bearing on 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 a little accustomed to the elemental recommendations of sheaf thought, homological algebra, and intricate differential geometry. within the ultimate chapters, a few very fresh questions and open difficulties are addressed--such as effects with regards to the finiteness of the canonical ring and the abundance conjecture, and effects describing the geometric constitution of Kahler kinds and their optimistic cones.

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