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 Differential Geometry

Author: Fangyang Zheng
Publisher: American Mathematical Soc.
ISBN: 0821829602
Category : Mathematics
Languages : en
Pages : 275

Book Description
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.

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.

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.

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.

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 Analytic Geometry

Author: Gerd Fischer
Publisher: Springer
ISBN: 354038121X
Category : Mathematics
Languages : en
Pages : 208

Book Description

From Holomorphic Functions to Complex Manifolds

Author: Klaus Fritzsche
Publisher: Springer Science & Business Media
ISBN: 146849273X
Category : Mathematics
Languages : en
Pages : 406

Book Description
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.

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.

Hodge Theory, Complex Geometry, and Representation Theory

Author: Mark Green
Publisher: American Mathematical Soc.
ISBN: 1470410125
Category : Mathematics
Languages : en
Pages : 314

Book Description
This monograph presents topics in Hodge theory and representation theory, two of the most active and important areas in contemporary mathematics. The underlying theme is the use of complex geometry to understand the two subjects and their relationships to one another--an approach that is complementary to what is in the literature. Finite-dimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinite-dimensional representation theory, specifically the discrete series and their limits, enters through the realization of these representations through complex geometry as pioneered by Schmid, and in the subsequent description of automorphic cohomology. For the latter topic, of particular importance is the recent work of Carayol that potentially introduces a new perspective in arithmetic automorphic representation theory. The present work gives a treatment of Carayol's work, and some extensions of it, set in a general complex geometric framework. Additional subjects include a description of the relationship between limiting mixed Hodge structures and the boundary orbit structure of Hodge domains, a general treatment of the correspondence spaces that are used to construct Penrose transforms and selected other topics from the recent literature. A co-publication of the AMS and CBMS.