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Hodge Theory (MN-49)

Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dung Tráng


This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from 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 Bloch–Beilinson 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 an ... More

Keywords: Hodge theory, contemporary mathematics, algebraic varieties, algebraic cycles, Kähler manifolds, Chow groups, sheaf cohomology, Shimura varieties, period mappings, Bloch–Beilinson conjecture

Bibliographic Information

Print publication date: 2014 Print ISBN-13: 9780691161341
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691161341.001.0001


Affiliations are at time of print publication.

Eduardo Cattani, author
University of Amherst

Fouad El Zein, author
Institut de Mathématiques de Jussieu, Université de Paris VII

Phillip A. Griffiths, author
Institute for Advanced Studies

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Chapter Three Mixed Hodge Structures

Fouad El Zein and Lê D˜ung Tráng

Chapter Five The Hodge Theory of Maps

Mark Andrea de Cataldo and Luca Migliorini Lectures 1–3 by Luca Migliorini

Chapter Six The Hodge Theory of Maps

Mark Andrea de Cataldo and Luca Migliorini Lectures 4–5 by Mark Andrea de Cataldo

Chapter Eight Variations of Mixed Hodge Structure

Patrick Brosnan and Fouad El Zein

Chapter Eleven Notes on Absolute Hodge Classes

François Charles and Christian Schnell

End Matter