By Jean-Pierre Demailly
This quantity is a spread of lectures given through the writer on the Park urban arithmetic Institute (Utah) in 2008, and on different events. the aim of this quantity is to explain analytic ideas precious within the learn 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 a bit accustomed to the fundamental techniques of sheaf concept, homological algebra, and complicated differential geometry. within the ultimate chapters, a few very contemporary 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 optimistic cones.
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