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A Course in Hodge Theory

2021 Hodge theory
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Release : 2021
Genre : Hodge theory
Kind : eBook
Book Rating : 002/5 ( reviews)

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Book Synopsis A Course in Hodge Theory by : Hossein Movasati

Download or read book A Course in Hodge Theory written by Hossein Movasati. This book was released on 2021. Available in PDF, EPUB and Kindle. Book excerpt: Offers an examination of the precursors of Hodge theory: first, the studies of elliptic and abelian integrals by Cauchy, Abel, Jacobi, and Riemann; and then the studies of two-dimensional multiple integrals by Poincare and Picard. The focus turns to the Hodge theory of affine hypersurfaces given by tame polynomials.

Introduction to Hodge Theory

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 407/5 ( reviews)

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Book Synopsis Introduction to Hodge Theory by : José Bertin

Download or read book Introduction to Hodge Theory written by José Bertin. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: Hodge theory originated as an application of harmonic theory to the study of the geometry of compact complex manifolds. The ideas have proved to be quite powerful, leading to fundamentally important results throughout algebraic geometry. This book consists of expositions of various aspects of modern Hodge theory. Its purpose is to provide the nonexpert reader with a precise idea of the current status of the subject. The three chapters develop distinct but closely related subjects:$L2$ Hodge theory and vanishing theorems; Frobenius and Hodge degeneration; variations of Hodge structures and mirror symmetry. The techniques employed cover a wide range of methods borrowed from the heart of mathematics: elliptic PDE theory, complex differential geometry, algebraic geometry incharacteristic $p$, cohomological and sheaf-theoretic methods, deformation theory of complex varieties, Calabi-Yau manifolds, singularity theory, etc. A special effort has been made to approach the various themes from their most na The reader should have some familiarity with differential and algebraic geometry, with other prerequisites varying by chapter. The book is suitable as an accompaniment to a second course in algebraic geometry.

Hodge Theory (MN-49)

2014-07-21 Mathematics
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Release : 2014-07-21
Genre : Mathematics
Kind : eBook
Book Rating : 348/5 ( reviews)

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Book Synopsis Hodge Theory (MN-49) by : Eduardo Cattani

Download or read book Hodge Theory (MN-49) written by Eduardo Cattani. This book was released on 2014-07-21. Available in PDF, EPUB and Kindle. Book excerpt: 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 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 Kähler 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 Bloch-Beilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendieck’s algebraic de Rham theorem. The advanced lectures address a Hodge-theoretic perspective on Shimura varieties, the spread philosophy in the study of algebraic cycles, absolute Hodge classes (including a new, self-contained proof of Deligne’s theorem on absolute Hodge cycles), and variation of mixed Hodge structures. The contributors include Patrick Brosnan, James Carlson, Eduardo Cattani, François Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, Lê Dũng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.

Introduction to Hodge theory

2007-05-01 Mathematics
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Release : 2007-05-01
Genre : Mathematics
Kind : eBook
Book Rating : 683/5 ( reviews)

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Book Synopsis Introduction to Hodge theory by : Herbert Clemens

Download or read book Introduction to Hodge theory written by Herbert Clemens. This book was released on 2007-05-01. Available in PDF, EPUB and Kindle. Book excerpt: This course will develop the parallel between the geometry of a compact, oriented differentiable manifold M endowed with a Riemannian metric and the geometry of a compact (oriented) complex manifold M with a Riemannian metric compatible with the complex structure. Such a metric is called a Kähler metric for M.

A Survey of the Hodge Conjecture

1999 Mathematics
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Release : 1999
Genre : Mathematics
Kind : eBook
Book Rating : 681/5 ( reviews)

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Book Synopsis A Survey of the Hodge Conjecture by : James Dominic Lewis

Download or read book A Survey of the Hodge Conjecture written by James Dominic Lewis. This book was released on 1999. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to a topic of central interest in transcendental algebraic geometry: the Hodge conjecture. Consisting of 15 lectures plus addenda and appendices, the volume is based on a series of lectures delivered by Professor Lewis at the Centre de Recherches Mathematiques (CRM). The book is a self-contained presentation, completely devoted to the Hodge conjecture and related topics. It includes many examples, and most results are completely proven or sketched. The motivation behind many of the results and background material is provided. This comprehensive approach to the book gives it a 'user-friendly' style. Readers need not search elsewhere for various results. The book is suitable for use as a text for a topics course in algebraic geometry. It includes an appendix by B. Brent Gordon.

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