This book provides a comprehensive and uptodate introduction to Hodge theoryone of the central and most vibrant areas of contemporary mathematicsfrom leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps. Of particular interest is the study of algebraic cycles, including the Hodge and BlochBeilinson Conjectures. Based on lectures delivered at the 2010 Summer School on Hodge Theory at the ICTP in Trieste, Italy, the book is intended for a broad group of students and researchers. The exposition is as accessible as possible and doesn't require a deep background. At the same time, the book presents some topics at the forefront of current research. The book is divided between introductory and advanced lectures. The introductory lectures address Kahler manifolds, variations of Hodge structure, mixed Hodge structures, the Hodge theory of maps, period domains and period mappings, algebraic cycles (up to and including the BlochBeilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendieck's algebraic de Rham theorem. The advanced lectures address a Hodgetheoretic perspective on Shimura varieties, the spread philosophy in the study of algebraic cycles, absolute Hodge classes (including a new, selfcontained proof of Deligne's theorem on absolute Hodge cycles), and variation of mixed Hodge structures. The contributors include Patrick Brosnan, James Carlson, Eduardo Cattani, Francois Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, Le D?ng Trang, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.
About Eduardo H. C. Cattani
Eduardo Cattani is professor of mathematics at the University of Massachusetts, Amherst. Fouad El Zein is a researcher at the Institut de Mathematiques de Jussieu, Universite de Paris VII. Phillip A. Griffiths is former director and professor emeritus of mathematics at the Institute for Advanced Study in Princeton. Le Dung Trang is professor emeritus of mathematics at the Universite d'AixMarseille.Details Book
Author  :  Eduardo H. C. Cattani 
Publisher  :  Princeton University Press 
Data Published  :  01 July 2014 
ISBN  :  0691161348 
EAN  :  9780691161341 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  608 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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