Hodge theory / / edited by Eduardo Cattani [and three others] ; Patrick Brosnan [and thirteen others], contributors

• Autore: Cattani Eduardo
• Pubblicazione: Princeton, New Jersey : , : Princeton University Press, , 2014; ©2014
• Edizione: Course Book
• Descrizione fisica: 1 online resource (608 p.)
• Disciplina: 514.223
• Soggetto topico: Manifolds (Mathematics)
• Soggetto non controllato: Abel–Jacobi map; Adélic lemmas; Albanese kernel; Bloch–Beilinson conjecture; Chow groups; Decomposition theorem; Deligne cohomology; Deligne's theorem; Galois action; Griffiths group; Griffiths' period map; Grothendieck's theorem; Hermitian structures; Hermitian symmetric domains; Hodge bundles; Hodge cycles; Hodge structure; Hodge structures; Hodge theory; Hodge-theoretic interpretations; Jacobian ideal; Kodaira–Spencer map; Kuga–Satake correspondence; Kähler manifolds; Kähler structures; Lefschetz decomposition; Poincaré residues; Schmid's orbit theorems; Shimura varieties; Thom–Whitney results; Torelli theorem; Verdier duality; absolute Hodge classes; abstract variations; algebraic cycles; algebraic equivalence; algebraic homology; algebraic maps; algebraic varieties; algebraicity; asymptotic behavior; coherent sheaves; cohomology; compact Kähler manifolds; complex manifolds; complex multiplication; conjectural filtration; contemporary mathematics; cycle class; cycle map; de Rham cohomology; de Rham theorem; differential forms; elliptic curves; equivalence relations; harmonic forms; holomorphicity; homological equivalence; horizontal distribution; horizontality; hypercohomology; hypersurfaces; intersection cohomology complex; intersection cohomology groups; invariant cycle theorem; linear algebra; local systems; mixed Hodge complex; mixed Hodge structure; mixed Hodge structures; monodromy; morphisms; nontrivial topological constraints; normal functions; period domains; period mappings; sheaf cohomology; smooth case; smooth projective varieties; spectral sequences; spread philosophy; spreads; symplectic structures; tangent space; topological invariants; variational Hodge conjecture; Čech cohomology
• Classificazione: SI 850
• Persona (resp. second.): CattaniEduardo; BrosnanPatrick
• Note generali: "Between 14 June and 2 July 2010, the Summer School on Hodge Theory and Related Topics and a related conference were hosted by the ICTP in Trieste, Italy."
• Nota di bibliografia: Includes bibliographical references at the end of each chapters and index.
• Nota di contenuto: Front matter -- Contributors -- Contents -- Preface -- Chapter One. Introduction to Kähler Manifolds / Cattani, Eduardo -- Chapter Two. From Sheaf Cohomology to the Algebraic de Rham Theorem / El Zein, Fouad / Tu, Loring W. -- Chapter Three. Mixed Hodge Structures / Zein, Fouad El / Tráng, Lê Dũng -- Chapter Four. Period Domains and Period Mappings / Carlson, James -- Chapter Five. The Hodge Theory of Maps / Cataldo, Mark Andrea de / Migliorini, Luca -- Chapter Six The Hodge Theory of Maps / Cataldo, Mark Andrea de / Migliorini, Luca -- Chapter Seven. Introduction to Variations of Hodge Structure / Cattani, Eduardo -- Chapter Eight. Variations of Mixed Hodge Structure / Brosnan, Patrick / Zein, Fouad El -- Chapter Nine. Lectures on Algebraic Cycles and Chow Groups / Murre, Jacob -- Chapter Ten. The Spread Philosophy in the Study of Algebraic Cycles / Green, Mark L. -- Chapter Eleven. Notes on Absolute Hodge Classes / Charles, François / Schnell, Christian -- Chapter Twelve. Shimura Varieties: A Hodge-Theoretic Perspective / Kerr, Matt -- Bibliography -- Index
• Sommario/riassunto: 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.
• Titolo autorizzato: Hodge theory
• ISBN: 1-4008-5147-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910786461403321
• Lo trovi qui: Univ. Federico II
• Serie: Mathematical notes (Princeton University Press) ; ; 49.