Cone And Contraction Theorem For Projective Morphisms Between Complex Analytic Spaces

The theory of minimal models, which was initiated by Shigefumi Mori around 1980, plays a crucial role in higher-dimensional algebraic geometry. It has been highly desirable to consider appropriate complex analytic generalizations. The main purpose of this book is to give a rigorous foundation of the minimal model program for projective morphisms between complex analytic spaces. More specifically, we establish the cone and contraction theorem for normal pairs in a complex analytic setting. It is a starting point for the minimal model program of complex analytic log canonical pairs. Based on this book, many results for higher-dimensional algebraic varieties have already been generalized for complex analytic spaces. The results obtained in this book are expected to be useful for the study of complex analytic singularities, degenerations of complex projective varieties, and so on. We note that our approach in this book depends heavily on the author's recent result on complex analytic generalizations of Kollar's vanishing theorem and torsion-freeness. This book is written not only for researchers, but also for graduate students who are interested in the theory of minimal models for projective morphisms of complex analytic spaces.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets