Complex Geometry

Author: Daniel Huybrechts
Publisher: Springer Science & Business Media
ISBN: 9783540212904
Category : Computers
Languages : en
Pages : 336

Book Description
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)

Complex Geometry

Author: Ian Reid
Publisher: Gingko Press
ISBN: 9781584237709
Category : Photography
Languages : en
Pages : 112

Book Description
Photographer and documentarian Ian Reid was born and raised in Fort Greene, Brooklyn. In 2018 he set out to photograph 23 public housing developments in Brooklyn from above. His goal was to preserve the architecture and to present the structures without any preconceived notions of what goes on within. The images are framed by the streets they are defined by, often showing how they look with the changing seasons. Gentrification and development have changed the surroundings of the public housing, but the buildings and its residents for the most part stay the same. Complex Geometry respects the true residents of Brooklyn and pays homage to where Reid grew up and still spends a great deal of his time.

Algebraic Geometry over the Complex Numbers

Author: Donu Arapura
Publisher: Springer Science & Business Media
ISBN: 1461418097
Category : Mathematics
Languages : en
Pages : 326

Book Description
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.

Geometry of Complex Numbers

Author: Hans Schwerdtfeger
Publisher: Courier Corporation
ISBN: 0486135861
Category : Mathematics
Languages : en
Pages : 228

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

Perspectives on Projective Geometry

Author: Jürgen Richter-Gebert
Publisher: Springer Science & Business Media
ISBN: 3642172865
Category : Mathematics
Languages : en
Pages : 573

Book Description
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.

The Geometry of Complex Domains

Author: Robert E. Greene
Publisher: Springer Science & Business Media
ISBN: 0817646221
Category : Mathematics
Languages : en
Pages : 310

Book Description
This work examines a rich tapestry of themes and concepts and provides a comprehensive treatment of an important area of mathematics, while simultaneously covering a broader area of the geometry of domains in complex space. At once authoritative and accessible, this text touches upon many important parts of modern mathematics: complex geometry, equivalent embeddings, Bergman and Kahler geometry, curvatures, differential invariants, boundary asymptotics of geometries, group actions, and moduli spaces. The Geometry of Complex Domains can serve as a “coming of age” book for a graduate student who has completed at least one semester or more of complex analysis, and will be most welcomed by analysts and geometers engaged in current research.

Complex Manifolds without Potential Theory

Author: Shiing-shen Chern
Publisher: Springer Science & Business Media
ISBN: 1468493442
Category : Mathematics
Languages : en
Pages : 158

Book Description
From the reviews of the second edition: "The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and so on. The differential geometrical methods of this theory were developed essentially under the influence of Professor S.-S. Chern's works. The present book is a second edition... It can serve as an introduction to, and a survey of, this theory and is based on the author's lectures held at the University of California and at a summer seminar of the Canadian Mathematical Congress.... The text is illustrated by many examples... The book is warmly recommended to everyone interested in complex differential geometry." #Acta Scientiarum Mathematicarum, 41, 3-4#

Hodge Theory and Complex Algebraic Geometry I:

Author: Claire Voisin
Publisher: Cambridge University Press
ISBN: 9780521718011
Category : Mathematics
Languages : en
Pages : 334

Book Description
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.

Complex Differential Geometry

Author: Fangyang Zheng
Publisher: American Mathematical Soc.
ISBN: 9780821888223
Category : Mathematics
Languages : en
Pages : 284

Book Description

Differential and Complex Geometry: Origins, Abstractions and Embeddings

Author: Raymond O. Wells, Jr.
Publisher: Springer
ISBN: 3319581848
Category : Mathematics
Languages : en
Pages : 320

Book Description
Differential and complex geometry are two central areas of mathematics with a long and intertwined history. This book, the first to provide a unified historical perspective of both subjects, explores their origins and developments from the sixteenth to the twentieth century. Providing a detailed examination of the seminal contributions to differential and complex geometry up to the twentieth-century embedding theorems, this monograph includes valuable excerpts from the original documents, including works of Descartes, Fermat, Newton, Euler, Huygens, Gauss, Riemann, Abel, and Nash. Suitable for beginning graduate students interested in differential, algebraic or complex geometry, this book will also appeal to more experienced readers.