Recent Advances In Hodge Theory
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Recent Advances in Hodge Theory
Author | : Matt Kerr,Gregory Pearlstein |
Publsiher | : Cambridge University Press |
Total Pages | : 533 |
Release | : 2016-02-04 |
Genre | : Mathematics |
ISBN | : 9781107546295 |
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Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.
Introduction to Hodge Theory
Author | : José Bertin |
Publsiher | : American Mathematical Soc. |
Total Pages | : 254 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821820400 |
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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.
Recent Advances in Hodge Theory Period Domains
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Author | : Anonim |
Publsiher | : Unknown |
Total Pages | : 135 |
Release | : 2016 |
Genre | : Electronic Book |
ISBN | : 1316533557 |
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Hodge Theory MN 49
Author | : Eduardo Cattani,Fouad El Zein,Phillip A. Griffiths,Lê Dũng Tráng |
Publsiher | : Princeton University Press |
Total Pages | : 608 |
Release | : 2014-07-21 |
Genre | : Mathematics |
ISBN | : 9781400851478 |
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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 MN 49
Author | : Eduardo Cattani,Fouad El Zein,Phillip A. Griffiths,Lê Dũng Tráng |
Publsiher | : Princeton University Press |
Total Pages | : 607 |
Release | : 2014-07-21 |
Genre | : Mathematics |
ISBN | : 9780691161341 |
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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.
Algebraic Cycles and Hodge Theory
Author | : Mark L. Green,Jacob P. Murre,Claire Voisin |
Publsiher | : Springer |
Total Pages | : 276 |
Release | : 2004-09-03 |
Genre | : Mathematics |
ISBN | : 9783540490463 |
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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.
Surveys on Recent Developments in Algebraic Geometry
Author | : Izzet Coskun,Tommaso de Fernex,Angela Gibney |
Publsiher | : American Mathematical Soc. |
Total Pages | : 370 |
Release | : 2017-07-12 |
Genre | : $K$-theory -- Higher algebraic $K$-theory -- $Q$- and plus-constructions |
ISBN | : 9781470435578 |
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The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.
Hodge Theory Complex Geometry and Representation Theory
Author | : Robert S. Doran,Greg Friedman,Scott Nollet |
Publsiher | : American Mathematical Soc. |
Total Pages | : 330 |
Release | : 2014 |
Genre | : Mathematics |
ISBN | : 9780821894156 |
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Contains carefully written expository and research articles. Expository papers include discussions of Noether-Lefschetz theory, algebraicity of Hodge loci, and the representation theory of SL2(R). Research articles concern the Hodge conjecture, Harish-Chandra modules, mirror symmetry, Hodge representations of Q-algebraic groups, and compactifications, distributions, and quotients of period domains.