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Pluripotential theory is a very powerful tool in geometry, complex
analysis and dynamics. This volume brings together the lectures
held at the 2011 CIME session on "pluripotential theory" in
Cetraro, Italy. This CIME course focused on complex Monge-Ampere
equations, applications of pluripotential theory to Kahler geometry
and algebraic geometry and to holomorphic dynamics. The
contributions provide an extensive description of the theory and
its very recent developments, starting from basic introductory
materials and concluding with open questions in current research.
This volume is an expansion of lectures given by the author at the
Park City Mathematics Institute (Utah) in 2008, and on other
occasions. The purpose of this volume is to describe analytic
techniques useful in the study of questions pertaining to linear
series, multiplier ideals, and vanishing theorems for algebraic
vector bundles. The author aims to be concise in his exposition,
assuming that the reader is already somewhat acquainted with the
basic concepts of sheaf theory, homological algebra, and complex
differential geometry. In the final chapters, some very recent
questions and open problems are addressed--such as results related
to the finiteness of the canonical ring and the abundance
conjecture, and results describing the geometric structure of
Kahler varieties and their positive cones.
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