Hodge Theory And Complex Algebraic Geometry I Volume 1
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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 | : 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 | : 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 | : Claire Voisin |
Publisher | : |
Total Pages | : 322 |
Release | : 2002 |
Genre | : Electronic books |
ISBN | : 9780511179754 |
Download Hodge theory and complex algebraic geometry I Book in PDF, Epub and Kindle
This is a completely self-contained modern introduction to Kaehlerian geometry and Hodge structure. The author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. Aimed at students, the text is complemented by exercises which provide useful results in complex algebraic geometry.
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 | : Claire Voisin |
Publisher | : |
Total Pages | : 322 |
Release | : 2002 |
Genre | : Geometry, Algebraic |
ISBN | : 9781107130708 |
Download Hodge Theory and Complex Algebraic Geometry Book in PDF, Epub and Kindle
This is a completely self-contained modern introduction to Kaehlerian geometry and Hodge structure. The author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. Aimed at students, the text is complemented by exercises which provide useful results in complex algebraic geometry.
Author | : Joseph L. Taylor |
Publisher | : American Mathematical Soc. |
Total Pages | : 530 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 082183178X |
Download Several Complex Variables with Connections to Algebraic Geometry and Lie Groups Book in PDF, Epub and Kindle
This text presents an integrated development of core material from several complex variables and complex algebraic geometry, leading to proofs of Serre's celebrated GAGA theorems relating the two subjects, and including applications to the representation theory of complex semisimple Lie groups. It includes a thorough treatment of the local theory using the tools of commutative algebra, an extensive development of sheaf theory and the theory of coherent analytic and algebraicsheaves, proofs of the main vanishing theorems for these categories of sheaves, and a complete proof of the finite dimensionality of the cohomology of coherent sheaves on compact varieties. The vanishing theorems have a wide variety of applications and these are covered in detail. Of particular interest arethe last three chapters, which are devoted to applications of the preceding material to the study of the structure theory and representation theory of complex semisimple Lie groups. Included are introductions to harmonic analysis, the Peter-Weyl theorem, Lie theory and the structure of Lie algebras, semisimple Lie algebras and their representations, algebraic groups and the structure of complex semisimple Lie groups. All of this culminates in Milicic's proof of the Borel-Weil-Bott theorem,which makes extensive use of the material developed earlier in the text. There are numerous examples and exercises in each chapter. This modern treatment of a classic point of view would be an excellent text for a graduate course on several complex variables, as well as a useful reference for theexpert.
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.