Introduction To Hodge Theory

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Introduction to Hodge Theory

José Bertin
Introduction to Hodge Theory Book PDF

Author : José Bertin
Publisher : American Mathematical Soc.
Page : 254 pages
File Size : 48,7 Mb
Release : 2002
Category : Mathematics
ISBN : 0821820400

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Introduction to Hodge Theory by José Bertin Pdf

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)

Eduardo Cattani,Fouad El Zein,Phillip A. Griffiths,Lê Dũng Tráng
Hodge Theory MN 49 Book PDF

Author : Eduardo Cattani,Fouad El Zein,Phillip A. Griffiths,Lê Dũng Tráng
Publisher : Princeton University Press
Page : 608 pages
File Size : 44,8 Mb
Release : 2014-07-21
Category : Mathematics
ISBN : 9781400851478

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Hodge Theory (MN-49) by Eduardo Cattani,Fouad El Zein,Phillip A. Griffiths,Lê Dũng Tráng Pdf

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.

Hodge Theory and Complex Algebraic Geometry I:

Claire Voisin
Hodge Theory and Complex Algebraic Geometry I Book PDF

Author : Claire Voisin
Publisher : Cambridge University Press
Page : 334 pages
File Size : 45,5 Mb
Release : 2007-12-20
Category : Mathematics
ISBN : 0521718015

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Hodge Theory and Complex Algebraic Geometry I: by Claire Voisin Pdf

This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions.

A Course in Hodge Theory

Hossein Movasati
A Course in Hodge Theory Book PDF

Author : Hossein Movasati
Publisher : Unknown
Page : 0 pages
File Size : 44,6 Mb
Release : 2021
Category : Hodge theory
ISBN : 157146400X

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A Course in Hodge Theory by Hossein Movasati Pdf

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.

Recent Advances in Hodge Theory

Matt Kerr,Gregory Pearlstein
Recent Advances in Hodge Theory Book PDF

Author : Matt Kerr,Gregory Pearlstein
Publisher : Cambridge University Press
Page : 533 pages
File Size : 46,5 Mb
Release : 2016-02-04
Category : Mathematics
ISBN : 9781107546295

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Recent Advances in Hodge Theory by Matt Kerr,Gregory Pearlstein Pdf

Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.

Mixed Hodge Structures

Chris A.M. Peters,Joseph H. M. Steenbrink
Mixed Hodge Structures Book PDF

Author : Chris A.M. Peters,Joseph H. M. Steenbrink
Publisher : Springer Science & Business Media
Page : 467 pages
File Size : 49,6 Mb
Release : 2008-02-27
Category : Mathematics
ISBN : 9783540770176

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Mixed Hodge Structures by Chris A.M. Peters,Joseph H. M. Steenbrink Pdf

This is comprehensive basic monograph on mixed Hodge structures. Building up from basic Hodge theory the book explains Delingne's mixed Hodge theory in a detailed fashion. Then both Hain's and Morgan's approaches to mixed Hodge theory related to homotopy theory are sketched. Next comes the relative theory, and then the all encompassing theory of mixed Hodge modules. The book is interlaced with chapters containing applications. Three large appendices complete the book.

Hodge Decomposition - A Method for Solving Boundary Value Problems

Günter Schwarz
Hodge Decomposition A Method for Solving Boundary Value Problems Book PDF

Author : Günter Schwarz
Publisher : Springer
Page : 161 pages
File Size : 50,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540494034

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Hodge Decomposition - A Method for Solving Boundary Value Problems by Günter Schwarz Pdf

Hodge theory is a standard tool in characterizing differ- ential complexes and the topology of manifolds. This book is a study of the Hodge-Kodaira and related decompositions on manifolds with boundary under mainly analytic aspects. It aims at developing a method for solving boundary value problems. Analysing a Dirichlet form on the exterior algebra bundle allows to give a refined version of the classical decomposition results of Morrey. A projection technique leads to existence and regularity theorems for a wide class of boundary value problems for differential forms and vector fields. The book links aspects of the geometry of manifolds with the theory of partial differential equations. It is intended to be comprehensible for graduate students and mathematicians working in either of these fields.

Hodge Theory, Complex Geometry, and Representation Theory

Mark Green, Phillip Griffiths,Matt Kerr
Hodge Theory Complex Geometry and Representation Theory Book PDF

Author : Mark Green, Phillip Griffiths,Matt Kerr
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 48,5 Mb
Release : 2013-11-05
Category : Mathematics
ISBN : 9781470410124

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Hodge Theory, Complex Geometry, and Representation Theory by Mark Green, Phillip Griffiths,Matt Kerr Pdf

This monograph presents topics in Hodge theory and representation theory, two of the most active and important areas in contemporary mathematics. The underlying theme is the use of complex geometry to understand the two subjects and their relationships to one another--an approach that is complementary to what is in the literature. Finite-dimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinite-dimensional representation theory, specifically the discrete series and their limits, enters through the realization of these representations through complex geometry as pioneered by Schmid, and in the subsequent description of automorphic cohomology. For the latter topic, of particular importance is the recent work of Carayol that potentially introduces a new perspective in arithmetic automorphic representation theory. The present work gives a treatment of Carayol's work, and some extensions of it, set in a general complex geometric framework. Additional subjects include a description of the relationship between limiting mixed Hodge structures and the boundary orbit structure of Hodge domains, a general treatment of the correspondence spaces that are used to construct Penrose transforms and selected other topics from the recent literature. A co-publication of the AMS and CBMS.

Period Mappings and Period Domains

James Carlson,Stefan Müller-Stach,Chris Peters
Period Mappings and Period Domains Book PDF

Author : James Carlson,Stefan Müller-Stach,Chris Peters
Publisher : Cambridge University Press
Page : 577 pages
File Size : 47,7 Mb
Release : 2017-08-24
Category : Mathematics
ISBN : 9781108422628

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Period Mappings and Period Domains by James Carlson,Stefan Müller-Stach,Chris Peters Pdf

An introduction to Griffiths' theory of period maps and domains, focused on algebraic, group-theoretic and differential geometric aspects.

Algebraic Cycles and Hodge Theory

Mark L. Green,Jacob P. Murre,Claire Voisin
Algebraic Cycles and Hodge Theory Book PDF

Author : Mark L. Green,Jacob P. Murre,Claire Voisin
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 52,8 Mb
Release : 1994-12-16
Category : Mathematics
ISBN : 354058692X

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Algebraic Cycles and Hodge Theory by Mark L. Green,Jacob P. Murre,Claire Voisin Pdf

The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. Thus the papers included in the proceedings are surveys and notes on the most important topics of this area of research. They include infinitesimal methods in Hodge theory; algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.

p-adic Hodge Theory

Bhargav Bhatt,Martin Olsson
p adic Hodge Theory Book PDF

Author : Bhargav Bhatt,Martin Olsson
Publisher : Springer Nature
Page : 325 pages
File Size : 46,8 Mb
Release : 2020-06-15
Category : Mathematics
ISBN : 9783030438449

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p-adic Hodge Theory by Bhargav Bhatt,Martin Olsson Pdf

This proceedings volume contains articles related to the research presented at the 2017 Simons Symposium on p-adic Hodge theory. This symposium was focused on recent developments in p-adic Hodge theory, especially those concerning integral questions and their connections to notions in algebraic topology. This volume features original research articles as well as articles that contain new research and survey some of these recent developments. It is the first of three volumes dedicated to p-adic Hodge theory.

Complex Geometry

Daniel Huybrechts
Complex Geometry Book PDF

Author : Daniel Huybrechts
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 48,7 Mb
Release : 2005
Category : Computers
ISBN : 3540212906

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Complex Geometry by Daniel Huybrechts Pdf

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

Hodge Theory and Complex Algebraic Geometry II:

Claire Voisin
Hodge Theory and Complex Algebraic Geometry II Book PDF

Author : Claire Voisin
Publisher : Cambridge University Press
Page : 362 pages
File Size : 48,5 Mb
Release : 2007-12-20
Category : Mathematics
ISBN : 0521718023

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Hodge Theory and Complex Algebraic Geometry II: by Claire Voisin Pdf

The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. The main results are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly, Nori's connectivity theorem, which generalizes the above. The last part deals with the relationships between Hodge theory and algebraic cycles. The text is complemented by exercises offering useful results in complex algebraic geometry. Also available: Volume I 0-521-80260-1 Hardback $60.00 C

An Introduction to Manifolds

Loring W. Tu
An Introduction to Manifolds Book PDF

Author : Loring W. Tu
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 50,6 Mb
Release : 2010-10-05
Category : Mathematics
ISBN : 9781441974006

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An Introduction to Manifolds by Loring W. Tu Pdf

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

A Survey of the Hodge Conjecture

James Dominic Lewis
A Survey of the Hodge Conjecture Book PDF

Author : James Dominic Lewis
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 40,7 Mb
Release : 1999
Category : Geometry, Algebraic
ISBN : 9780821805688

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A Survey of the Hodge Conjecture by James Dominic Lewis Pdf

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.