Complex Analytic Cycles : Basic Results on Complex Geometry and Foundations f...

Complex Analytic Cycles : Basic Results on Complex Geometry and Foundations for the Study of Cycles, Paperback by Barlet, Daniel; Magnússon, Jón; Huckleberry, Alan (TRN), ISBN 3030311651, ISBN-13 9783030311650, Like New Used, Free shipping in the US

Th consists of a presentation from scratch of cycle space methodology incomplex geometry. Applications in various contexts are given. A significant portionof th is devoted to material which is important in the general area of complexanalysis. In this regard, a geometric approach is used to obtain fundamental results such as the local parameterization theorem, Lelong\' s Theorem and Remmert\'s direct image theorem. Methods involving cycle spaces have been used in complex geometry for some forty years. The purpose of th is to systematically explain these methods in a way which is accessible to graduate students in mathematics as well as to research mathematicians. After the background material which is presented in the initial chapters, families of cycles are treated in the last most important part of th. Their topological aspects are developed in a systematic way and some basic, important applications of analytic families of cycles are given. The construction of the cycle space as a complex space, along with numerous important applications, is given in the second volume. The present book is a translation of the French version that was published in 2014 by the French Mathematical Society.