By Jean-Pierre Demailly
This quantity is a variety 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 strategies helpful within the learn of questions relating 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 conversant in the fundamental suggestions of sheaf concept, homological algebra, and complicated differential geometry. within the ultimate chapters, a few very fresh questions and open difficulties are addressed--such as effects concerning the finiteness of the canonical ring and the abundance conjecture, and effects describing the geometric constitution of Kahler forms and their confident cones.
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