By Jean-Pierre Demailly
This quantity is a variety 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 thoughts worthy 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 just a little conversant in the fundamental options of sheaf idea, homological algebra, and intricate differential geometry. within the ultimate chapters, a few very contemporary questions and open difficulties are addressed--such as effects on the topic of the finiteness of the canonical ring and the abundance conjecture, and effects describing the geometric constitution of Kahler types and their optimistic cones.
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