Hodge Theory 1st Edition by Eduardo Cattani,Fouad El Zein,Phillip A Griffiths,Le Dung Trang ISBN 0691161348 9780691161341

Hodge Theory 1st Edition by Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, Lê Dũng Tráng – Ebook PDF Instant Download/Delivery: 0691161348, 9780691161341

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Product details:

ISBN 10: 0691161348

ISBN 13: 9780691161341 

Author: Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, Lê Dũng Tráng 

Hodge Theory (1st Edition) by Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng is a comprehensive and scholarly text that provides an in-depth exploration of Hodge theory, which is a central topic in algebraic geometry and mathematical analysis. The book is aimed at advanced students and researchers in mathematics, especially those interested in the intersection of algebraic geometry, topology, and differential geometry.

The text introduces the concept of Hodge theory, focusing on its applications to complex algebraic varieties and the study of their topology. It covers key topics such as the Hodge decomposition theorem, the study of harmonic forms, and the interaction between algebraic geometry and topology. The authors also discuss the relationship between algebraic cycles, cohomology, and the underlying structure of algebraic varieties.

The book is structured to present both theoretical aspects and practical applications of Hodge theory. It provides rigorous proofs, along with a variety of examples, to help readers develop a deeper understanding of the subject. The book is a valuable resource for anyone studying advanced topics in algebraic geometry, particularly those with an interest in the intersection of geometry, topology, and analysis.

Given the advanced nature of the material, Hodge Theory is best suited for graduate students or professional mathematicians with a strong background in algebraic geometry, differential geometry, and complex analysis.

Table of contents:

1 Kähler Manifolds by E. Cattani
2 The Algebraic de Rham Theorem by F. El Zein and L. Tu
3 Mixed Hodge Structures by F. El Zein and Lê D. T.
4 Period domains by J. Carlson
5 Hodge theory of maps, Part I by L. Migliorini
6 Hodge theory of maps, Part II by M. A. de Cataldo
7 Variations of Hodge Structure by E. Cattani
8 Variations of Mixed Hodge Structure by P. Brosnan and F. El Zein
Introduction
9 Algebraic Cycles and Chow groups by J. Murre
10 Spreads and Algebraic Cycles by M. L. Green
11 Absolute Hodge Classes by F. Charles and C. Schnell
12 Shimura Varieties by M. Kerr

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Tags: Eduardo Cattani, Fouad El Zein, Phillip A Griffiths, Le Dung Trang, Hodge, Theory