Global Aspects of Complex Geometry

Global Aspects of Complex Geometry
Author: Fabrizio Catanese
Publisher: Springer Science & Business Media
Total Pages: 508
Release: 2006-09-29
Genre: Mathematics
ISBN: 3540354808

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This collection of surveys present an overview of recent developments in Complex Geometry. Topics range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kähler geometry, and group actions to Hodge theory and characteristic p-geometry. Written by established experts this book will be a must for mathematicians working in Complex Geometry

Complex Differential Geometry

Complex Differential Geometry
Author: Fangyang Zheng
Publisher: American Mathematical Soc.
Total Pages: 275
Release: 2000
Genre: Mathematics
ISBN: 0821829602

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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.

Complex Geometry

Complex Geometry
Author: Daniel Huybrechts
Publisher: Springer Science & Business Media
Total Pages: 336
Release: 2005
Genre: Computers
ISBN: 9783540212904

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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)

Algebraic Geometry over the Complex Numbers

Algebraic Geometry over the Complex Numbers
Author: Donu Arapura
Publisher: Springer Science & Business Media
Total Pages: 326
Release: 2012-02-15
Genre: Mathematics
ISBN: 1461418097

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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.

Perspectives on Projective Geometry

Perspectives on Projective Geometry
Author: Jürgen Richter-Gebert
Publisher: Springer Science & Business Media
Total Pages: 573
Release: 2011-02-04
Genre: Mathematics
ISBN: 3642172865

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Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.

Geometry of Complex Numbers

Geometry of Complex Numbers
Author: Hans Schwerdtfeger
Publisher: Courier Corporation
Total Pages: 228
Release: 2012-05-23
Genre: Mathematics
ISBN: 0486135861

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Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Manifolds, Sheaves, and Cohomology

Manifolds, Sheaves, and Cohomology
Author: Torsten Wedhorn
Publisher: Springer
Total Pages: 366
Release: 2016-07-25
Genre: Mathematics
ISBN: 3658106336

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This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.

Current Topics in Complex Algebraic Geometry

Current Topics in Complex Algebraic Geometry
Author: Charles Herbert Clemens
Publisher: Cambridge University Press
Total Pages: 180
Release: 1995
Genre: Mathematics
ISBN: 9780521562447

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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.

Complex and Differential Geometry

Complex and Differential Geometry
Author: Wolfgang Ebeling
Publisher: Springer Science & Business Media
Total Pages: 424
Release: 2011-06-27
Genre: Mathematics
ISBN: 3642203000

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This volume contains the Proceedings of the conference "Complex and Differential Geometry 2009", held at Leibniz Universität Hannover, September 14 - 18, 2009. It was the aim of this conference to bring specialists from differential geometry and (complex) algebraic geometry together and to discuss new developments in and the interaction between these fields. Correspondingly, the articles in this book cover a wide area of topics, ranging from topics in (classical) algebraic geometry through complex geometry, including (holomorphic) symplectic and poisson geometry, to differential geometry (with an emphasis on curvature flows) and topology.

Complex Geometry

Complex Geometry
Author: Ingrid Bauer
Publisher: Springer Science & Business Media
Total Pages: 357
Release: 2011-06-28
Genre: Mathematics
ISBN: 3642562027

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This volume contains a collection of research papers dedicated to Hans Grauert on the occasion of his seventieth birthday. Hans Grauert is a pioneer in modern complex analysis, continuing the il lustrious German tradition in function theory of several complex variables of Weierstrass, Behnke, Thullen, Stein, Siegel, and many others. When Grauert came on the scene in the early 1950's, function theory was going through a revolutionary period with the geometric theory of complex spaces still in its embryonic stage. A rich theory evolved with the joint efforts of many great mathematicians including Oka, Kodaira, Cartan, and Serre. The Car tan Seminar in Paris and the Kodaira Seminar provided important venues an for its development. Grauert, together with Andreotti and Remmert, took active part in the latter. In his career he has nurtured a great number of his own doctoral students as well as other young mathematicians in his field from allover the world. For a couple of decades his work blazed the trail and set the research agenda in several complex variables worldwide. Among his many fundamentally important contributions, which are too numerous to completely enumerate here, are: 1. The complete clarification of various notions of complex spaces. 2. The solution of the general Levi problem and his work on pseudo convexity for general manifolds. 3. The theory of exceptional analytic sets. 4. The Oka principle for holomorphic bundles. 5. The proof of the Mordell conjecture for function fields. 6. The direct image theorem for coherent sheaves.