Hodge Theory And Complex Algebraic Geometry I
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Author | : Claire Voisin |
Publisher | : Cambridge University Press |
Total Pages | : 336 |
Release | : 2002-12-05 |
Genre | : Mathematics |
ISBN | : 1139437690 |
Download Hodge Theory and Complex Algebraic Geometry I: Volume 1 Book in PDF, Epub and Kindle
The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.
Author | : Claire Voisin |
Publisher | : Cambridge University Press |
Total Pages | : 334 |
Release | : 2007-12-20 |
Genre | : Mathematics |
ISBN | : 9780521718011 |
Download Hodge Theory and Complex Algebraic Geometry I: Book in PDF, Epub and Kindle
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 |
Total Pages | : 362 |
Release | : 2007-12-20 |
Genre | : Mathematics |
ISBN | : 9780521718028 |
Download Hodge Theory and Complex Algebraic Geometry II: Book in PDF, Epub and Kindle
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 | : Donu Arapura |
Publisher | : Springer Science & Business Media |
Total Pages | : 326 |
Release | : 2012-02-15 |
Genre | : Mathematics |
ISBN | : 1461418097 |
Download Algebraic Geometry over the Complex Numbers Book in PDF, Epub and Kindle
This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.
Author | : Daniel Huybrechts |
Publisher | : Springer Science & Business Media |
Total Pages | : 336 |
Release | : 2005 |
Genre | : Computers |
ISBN | : 9783540212904 |
Download Complex Geometry Book in PDF, Epub and Kindle
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)
Author | : Mark Green |
Publisher | : American Mathematical Soc. |
Total Pages | : 314 |
Release | : 2013-11-05 |
Genre | : Mathematics |
ISBN | : 1470410125 |
Download Hodge Theory, Complex Geometry, and Representation Theory Book in PDF, Epub and Kindle
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 | : José Bertin |
Publisher | : American Mathematical Soc. |
Total Pages | : 254 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9780821820407 |
Download Introduction to Hodge Theory Book in PDF, Epub and Kindle
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 | : Chris A.M. Peters |
Publisher | : Springer Science & Business Media |
Total Pages | : 467 |
Release | : 2008-02-27 |
Genre | : Mathematics |
ISBN | : 3540770178 |
Download Mixed Hodge Structures Book in PDF, Epub and Kindle
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.
Author | : Voisin |
Publisher | : |
Total Pages | : |
Release | : 2014-01-01 |
Genre | : Hodge theory |
ISBN | : 9780521170321 |
Download Hodge Theory and Complex Algebraic Geometry Book in PDF, Epub and Kindle
The second of two volumes offering a modern account of Kaehlerian geometry and Hodge theory for researchers in algebraic and differential geometry.
Author | : James Carlson |
Publisher | : Cambridge University Press |
Total Pages | : 577 |
Release | : 2017-08-24 |
Genre | : Mathematics |
ISBN | : 1108422624 |
Download Period Mappings and Period Domains Book in PDF, Epub and Kindle
An introduction to Griffiths' theory of period maps and domains, focused on algebraic, group-theoretic and differential geometric aspects.