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Algebraic Geometry over the Complex Numbers

2012-02-15 Mathematics
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Release : 2012-02-15
Genre : Mathematics
Kind : eBook
Book Rating : 097/5 ( reviews)

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Book Synopsis Algebraic Geometry over the Complex Numbers by : Donu Arapura

Download or read book Algebraic Geometry over the Complex Numbers written by Donu Arapura. This book was released on 2012-02-15. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Complex Geometry

2005 Computers
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Release : 2005
Genre : Computers
Kind : eBook
Book Rating : 904/5 ( reviews)

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Book Synopsis Complex Geometry by : Daniel Huybrechts

Download or read book Complex Geometry written by Daniel Huybrechts. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: 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)

Principles of Algebraic Geometry

2014-08-21 Mathematics
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Release : 2014-08-21
Genre : Mathematics
Kind : eBook
Book Rating : 32X/5 ( reviews)

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Book Synopsis Principles of Algebraic Geometry by : Phillip Griffiths

Download or read book Principles of Algebraic Geometry written by Phillip Griffiths. This book was released on 2014-08-21. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds.

Hodge Theory and Complex Algebraic Geometry I:

2007-12-20 Mathematics
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Release : 2007-12-20
Genre : Mathematics
Kind : eBook
Book Rating : 011/5 ( reviews)

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Book Synopsis Hodge Theory and Complex Algebraic Geometry I: by : Claire Voisin

Download or read book Hodge Theory and Complex Algebraic Geometry I: written by Claire Voisin. This book was released on 2007-12-20. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Several Complex Variables with Connections to Algebraic Geometry and Lie Groups

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 78X/5 ( reviews)

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Book Synopsis Several Complex Variables with Connections to Algebraic Geometry and Lie Groups by : Joseph L. Taylor

Download or read book Several Complex Variables with Connections to Algebraic Geometry and Lie Groups written by Joseph L. Taylor. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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