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Author: Gary Kennedy Publisher: American Mathematical Soc. ISBN: 1470409909 Category : Mathematics Languages : en Pages : 148
Book Description
This volume contains the proceedings of a conference on Hodge Theory and Classical Algebraic Geometry, held May 13-15, 2013, at The Ohio State University, Columbus, OH. Hodge theory is a powerful tool for the study and classification of algebraic varieties. This volume surveys recent progress in Hodge theory, its generalizations, and applications. The topics range from more classical aspects of Hodge theory to modern developments in compactifications of period domains, applications of Saito's theory of mixed Hodge modules, and connections with derived category theory and non-commutative motives.
Author: Gary Kennedy Publisher: American Mathematical Soc. ISBN: 1470409909 Category : Mathematics Languages : en Pages : 148
Book Description
This volume contains the proceedings of a conference on Hodge Theory and Classical Algebraic Geometry, held May 13-15, 2013, at The Ohio State University, Columbus, OH. Hodge theory is a powerful tool for the study and classification of algebraic varieties. This volume surveys recent progress in Hodge theory, its generalizations, and applications. The topics range from more classical aspects of Hodge theory to modern developments in compactifications of period domains, applications of Saito's theory of mixed Hodge modules, and connections with derived category theory and non-commutative motives.
Author: Gary Kennedy Publisher: ISBN: 9781470426712 Category : Geometry, Algebraic Languages : en Pages : 137
Book Description
This volume contains the proceedings of a conference on Hodge Theory and Classical Algebraic Geometry, held May 13-15, 2013, at The Ohio State University, Columbus, OH. Hodge theory is a powerful tool for the study and classification of algebraic varieties. This volume surveys recent progress in Hodge theory, its generalizations, and applications. The topics range from more classical aspects of Hodge theory to modern developments in compactifications of period domains, applications of Saito's theory of mixed Hodge modules, and connections with derived category theory and non-commutative motive.
Author: Claire Voisin Publisher: Cambridge University Press ISBN: 9780521718011 Category : Mathematics Languages : en Pages : 334
Book Description
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.
Author: Claire Voisin Publisher: Cambridge University Press ISBN: 9780521718028 Category : Mathematics Languages : en Pages : 362
Book Description
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 $60.00 C
Author: Robin Hartshorne Publisher: Springer Science & Business Media ISBN: 1475738498 Category : Mathematics Languages : en Pages : 511
Book Description
An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Book Description
Hodge theory originated as an application of harmonic theory to the study of the geometry of compact complex manifolds. The ideas have proved to be quite powerful, leading to fundamentally important results throughout algebraic geometry. This book consists of expositions of various aspects of modern Hodge theory. Its purpose is to provide the nonexpert reader with a precise idea of the current status of the subject. The three chapters develop distinct but closely related subjects:$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.
Author: Mark Green Publisher: American Mathematical Soc. ISBN: 1470410125 Category : Mathematics Languages : en Pages : 314
Book Description
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.
Author: Eduardo H.C. Cattani Publisher: Springer ISBN: 3540477942 Category : Mathematics Languages : en Pages : 182
Book Description
Over the past 2O years classical Hodge theory has undergone several generalizations of great interest in algebraic geometry. The papers in this volume reflect the recent developments in the areas of: mixed Hodge theory on the cohomology of singular and open varieties, on the rational homotopy of algebraic varieties, on the cohomology of a link, and on the vanishing cycles; L -realization of the intersection cohomology for the cases of singular varieties and smooth varieties with degenerating coefficients; applications of cubical hyperresolutions and of iterated integrals; asymptotic behavior of degenerating variations of Hodge structure; the geometric realization of maximal variations; and variations of mixed Hodge structure. N
Author: Gary Kennedy
Author: Gary Kennedy
Author: Gary Kennedy
Author: Claire Voisin
Author: Claire Voisin
Author: Phillip A. Griffiths
Author: Robin Hartshorne
Author: José Bertin
Author: Matt Kerr
Author: Mark Green
Author: Eduardo H.C. Cattani