By Jean-Pierre Demailly

This quantity is a variety 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 strategies worthy within the research 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 familiar with the fundamental options of sheaf concept, homological algebra, and intricate differential geometry. within the ultimate chapters, a few very contemporary 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 types and their confident cones.

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