Algebraic And Complex Geometry

Author : Donu Arapura
Publisher : Springer Science & Business Media
Page : 326 pages
File Size : 52,5 Mb
Release : 2012-02-15
Category : Mathematics
ISBN : 9781461418092

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Algebraic Geometry over the Complex Numbers by Donu Arapura Pdf

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
Page : 336 pages
File Size : 47,9 Mb
Release : 2005
Category : Computers
ISBN : 3540212906

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Complex Geometry by Daniel Huybrechts Pdf

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 : Charles Herbert Clemens,Janos Kollár
Publisher : Cambridge University Press
Page : 180 pages
File Size : 49,5 Mb
Release : 1995
Category : Mathematics
ISBN : 0521562449

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Current Topics in Complex Algebraic Geometry by Charles Herbert Clemens,Janos Kollár Pdf

The 1992/93 academic year at the Mathematical Sciences Research Institute was devoted to complex algebraic geometry. This volume collects survey articles that arose from this event, which took place at a time when algebraic geometry was undergoing a major change. The editors of the volume, Herbert Clemens and János Kollár, chaired the organizing committee. This book gives a good idea of the intellectual content of the special year and of the workshops. Its articles represent very well the change of direction and branching out witnessed by algebraic geometry in the last few years.

Author : Phillip Griffiths,Joseph Harris
Publisher : John Wiley & Sons
Page : 837 pages
File Size : 52,8 Mb
Release : 2014-08-21
Category : Mathematics
ISBN : 9781118626320

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Principles of Algebraic Geometry by Phillip Griffiths,Joseph Harris Pdf

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.

Author : Claire Voisin
Publisher : Cambridge University Press
Page : 334 pages
File Size : 55,7 Mb
Release : 2007-12-20
Category : Mathematics
ISBN : 0521718015

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Hodge Theory and Complex Algebraic Geometry I: by Claire Voisin Pdf

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 : Fangyang Zheng
Publisher : American Mathematical Soc.
Page : 275 pages
File Size : 44,9 Mb
Release : 2000
Category : Complex manifolds
ISBN : 9780821829608

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Complex Differential Geometry by Fangyang Zheng Pdf

Discusses the differential geometric aspects of complex manifolds. This work contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. It discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles. It also gives a brief account of the surface classification theory.

Author : James Carlson,Stefan Müller-Stach,Chris Peters
Publisher : Cambridge University Press
Page : 577 pages
File Size : 42,8 Mb
Release : 2017-08-24
Category : Mathematics
ISBN : 9781108422628

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Period Mappings and Period Domains by James Carlson,Stefan Müller-Stach,Chris Peters Pdf

An introduction to Griffiths' theory of period maps and domains, focused on algebraic, group-theoretic and differential geometric aspects.

Author : Joseph L. Taylor
Publisher : American Mathematical Soc.
Page : 530 pages
File Size : 55,5 Mb
Release : 2002
Category : Functions of several complex variables
ISBN : 9780821831786

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

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 : Igor Rostislavovich Shafarevich
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 49,9 Mb
Release : 1994
Category : Mathematics
ISBN : 3540575545

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Basic Algebraic Geometry 2 by Igor Rostislavovich Shafarevich Pdf

The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with Volume 1 the author has revised the text and added new material, e.g. a section on real algebraic curves. Although the material is more advanced than in Volume 1 the algebraic apparatus is kept to a minimum making the book accessible to non-specialists. It can be read independently of Volume 1 and is suitable for beginning graduate students in mathematics as well as in theoretical physics.

Author : Thomas Peternell,Joichi Miyaoka
Publisher : Birkhäuser
Page : 221 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034888936

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Geometry of Higher Dimensional Algebraic Varieties by Thomas Peternell,Joichi Miyaoka Pdf

This book is based on lecture notes of a seminar of the Deutsche Mathematiker Vereinigung held by the authors at Oberwolfach from April 2 to 8, 1995. It gives an introduction to the classification theory and geometry of higher dimensional complex-algebraic varieties, focusing on the tremendeous developments of the sub ject in the last 20 years. The work is in two parts, with each one preceeded by an introduction describing its contents in detail. Here, it will suffice to simply ex plain how the subject matter has been divided. Cum grano salis one might say that Part 1 (Miyaoka) is more concerned with the algebraic methods and Part 2 (Peternell) with the more analytic aspects though they have unavoidable overlaps because there is no clearcut distinction between the two methods. Specifically, Part 1 treats the deformation theory, existence and geometry of rational curves via characteristic p, while Part 2 is principally concerned with vanishing theorems and their geometric applications. Part I Geometry of Rational Curves on Varieties Yoichi Miyaoka RIMS Kyoto University 606-01 Kyoto Japan Introduction: Why Rational Curves? This note is based on a series of lectures given at the Mathematisches Forschungsin stitut at Oberwolfach, Germany, as a part of the DMV seminar "Mori Theory". The construction of minimal models was discussed by T.

Author : K. Kodaira
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461385905

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Complex Manifolds and Deformation of Complex Structures by K. Kodaira Pdf

This book is an introduction to the theory of complex manifolds and their deformations. Deformation of the complex structure of Riemann surfaces is an idea which goes back to Riemann who, in his famous memoir on Abelian functions published in 1857, calculated the number of effective parameters on which the deformation depends. Since the publication of Riemann's memoir, questions concerning the deformation of the complex structure of Riemann surfaces have never lost their interest. The deformation of algebraic surfaces seems to have been considered first by Max Noether in 1888 (M. Noether: Anzahl der Modulen einer Classe algebraischer Fliichen, Sitz. K6niglich. Preuss. Akad. der Wiss. zu Berlin, erster Halbband, 1888, pp. 123-127). However, the deformation of higher dimensional complex manifolds had been curiously neglected for 100 years. In 1957, exactly 100 years after Riemann's memoir, Frolicher and Nijenhuis published a paper in which they studied deformation of higher dimensional complex manifolds by a differential geometric method and obtained an important result. (A. Fr61icher and A. Nijenhuis: A theorem on stability of complex structures, Proc. Nat. Acad. Sci., U.S.A., 43 (1957), 239-241).

Author : Kunihiko Kodaira,W. L. Jr Baily,T. Shioda
Publisher : CUP Archive
Page : 424 pages
File Size : 40,5 Mb
Release : 1977
Category : Mathematics
ISBN : 0521217776

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Complex Analysis and Algebraic Geometry by Kunihiko Kodaira,W. L. Jr Baily,T. Shioda Pdf

The articles in this volume cover some developments in complex analysis and algebraic geometry. The book is divided into three parts. Part I includes topics in the theory of algebraic surfaces and analytic surface. Part II covers topics in moduli and classification problems, as well as structure theory of certain complex manifolds. Part III is devoted to various topics in algebraic geometry analysis and arithmetic. A survey article by Ueno serves as an introduction to the general background of the subject matter of the volume. The volume was written for Kunihiko Kodaira on the occasion of his sixtieth birthday, by his friends and students. Professor Kodaira was one of the world's leading mathematicians in algebraic geometry and complex manifold theory: and the contributions reflect those concerns.

Author : Enrique Ramirez de Arellano
Publisher : Springer
Page : 192 pages
File Size : 52,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540469131

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Algebraic Geometry and Complex Analysis by Enrique Ramirez de Arellano Pdf

Author : David Mumford
Publisher : Springer
Page : 208 pages
File Size : 44,6 Mb
Release : 1976
Category : Mathematics
ISBN : STANFORD:36105031747863

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Algebraic Geometry I by David Mumford Pdf

From the reviews: "Although several textbooks on modern algebraic geometry have been published in the meantime, Mumford's "Volume I" is, together with its predecessor the red book of varieties and schemes, now as before one of the most excellent and profound primers of modern algebraic geometry. Both books are just true classics!" Zentralblatt

Author : Klaus Fritzsche,Hans Grauert
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468492736

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From Holomorphic Functions to Complex Manifolds by Klaus Fritzsche,Hans Grauert Pdf

This introduction to the theory of complex manifolds covers the most important branches and methods in complex analysis of several variables while completely avoiding abstract concepts involving sheaves, coherence, and higher-dimensional cohomology. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Each chapter contains a variety of examples and exercises.