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Global Aspects Of Complex Geometry
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Book Synopsis Global Aspects of Complex Geometry by : Fabrizio Catanese
Download or read book Global Aspects of Complex Geometry written by Fabrizio Catanese and published by Springer Science & Business Media. This book was released on 2006-09-29 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Complex Differential Geometry by : Fangyang Zheng
Download or read book Complex Differential Geometry written by Fangyang Zheng and published by American Mathematical Soc.. This book was released on 2000 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Complex Geometry by : Daniel Huybrechts
Download or read book Complex Geometry written by Daniel Huybrechts and published by Springer Science & Business Media. This book was released on 2005 with total page 336 pages. 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)
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 and published by Springer Science & Business Media. This book was released on 2012-02-15 with total page 326 pages. 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.
Author :Jürgen Richter-Gebert Publisher :Springer Science & Business Media ISBN 13 :3642172865 Total Pages :573 pages Book Rating :4.6/5 (421 download)
Book Synopsis Perspectives on Projective Geometry by : Jürgen Richter-Gebert
Download or read book Perspectives on Projective Geometry written by Jürgen Richter-Gebert and published by Springer Science & Business Media. This book was released on 2011-02-04 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometry of Complex Numbers by : Hans Schwerdtfeger
Download or read book Geometry of Complex Numbers written by Hans Schwerdtfeger and published by Courier Corporation. This book was released on 2012-05-23 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.
Book Synopsis Current Topics in Complex Algebraic Geometry by : Charles Herbert Clemens
Download or read book Current Topics in Complex Algebraic Geometry written by Charles Herbert Clemens and published by Cambridge University Press. This book was released on 1995 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Complex and Differential Geometry by : Wolfgang Ebeling
Download or read book Complex and Differential Geometry written by Wolfgang Ebeling and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Manifolds, Sheaves, and Cohomology by : Torsten Wedhorn
Download or read book Manifolds, Sheaves, and Cohomology written by Torsten Wedhorn and published by Springer. This book was released on 2016-07-25 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Proceedings of the International Conference on Complex Geometry and Related Fields by : Zhijie Chen
Download or read book Proceedings of the International Conference on Complex Geometry and Related Fields written by Zhijie Chen and published by American Mathematical Soc.. This book was released on 2007 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: In commemoration and celebration of the tenth anniversary of the Institute of Mathematics at East China Normal University, an International Conference on complex geometry and related fields recently convened. This collection presents some of the conference highlights, dealing with various and significant topics of differential and algebraic geometry, while exploring their connections to number theory and mathematical physics. Information for our distributors: Titles in this series are co-published with International Press, Cambridge, MA.
Download or read book Complex Geometry written by Ingrid Bauer and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Projective Geometry and Formal Geometry by : Lucian Badescu
Download or read book Projective Geometry and Formal Geometry written by Lucian Badescu and published by Birkhäuser. This book was released on 2012-12-06 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this monograph is to introduce the reader to modern methods of projective geometry involving certain techniques of formal geometry. Some of these methods are illustrated in the first part through the proofs of a number of results of a rather classical flavor, involving in a crucial way the first infinitesimal neighbourhood of a given subvariety in an ambient variety. Motivated by the first part, in the second formal functions on the formal completion X/Y of X along a closed subvariety Y are studied, particularly the extension problem of formal functions to rational functions. The formal scheme X/Y, introduced to algebraic geometry by Zariski and Grothendieck in the 1950s, is an analogue of the concept of a tubular neighbourhood of a submanifold of a complex manifold. It is very well suited to study the given embedding Y\subset X. The deep relationship of formal geometry with the most important connectivity theorems in algebraic geometry, or with complex geometry, is also studied. Some of the formal methods are illustrated and applied to homogeneous spaces. The book contains a lot of results obtained over the last thirty years, many of which never appeared in a monograph or textbook. It addresses to algebraic geometers as well as to those interested in using methods of algebraic geometry.
Book Synopsis Hodge Theory, Complex Geometry, and Representation Theory by : Mark Green
Download or read book Hodge Theory, Complex Geometry, and Representation Theory written by Mark Green and published by American Mathematical Soc.. This book was released on 2013-11-05 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Surveys on Recent Developments in Algebraic Geometry by : Izzet Coskun
Download or read book Surveys on Recent Developments in Algebraic Geometry written by Izzet Coskun and published by American Mathematical Soc.. This book was released on 2017-07-12 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.
Book Synopsis Geometry and Complex Variables by : S. Coen
Download or read book Geometry and Complex Variables written by S. Coen and published by CRC Press. This book was released on 1991-06-03 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference presents the proceedings of an international meeting on the occasion of theUniversity of Bologna's ninth centennial-highlighting the latest developments in the field ofgeometry and complex variables and new results in the areas of algebraic geometry, differential geometry, and analytic functions of one or several complex variables.Building upon the rich tradition of the University of Bologna's great mathematics teachers, thisvolume contains new studies on the history of mathematics, including the algebraic geometrywork of F. Enriques, B. Levi, and B. Segre ... complex function theory ideas of L. Fantappie, B. Levi, S. Pincherle, and G. Vitali ... series theory and logarithm theory contributions of P.Mengoli and S. Pincherle ... and much more. Additionally, the book lists all the University ofBologna's mathematics professors-from 1860 to 1940-with precise indications of eachcourse year by year.Including survey papers on combinatorics, complex analysis, and complex algebraic geometryinspired by Bologna's mathematicians and current advances, Geometry and ComplexVariables illustrates the classic works and ideas in the field and their influence on today'sresearc
Book Synopsis Riemann Surfaces by Way of Complex Analytic Geometry by : Dror Varolin
Download or read book Riemann Surfaces by Way of Complex Analytic Geometry written by Dror Varolin and published by American Mathematical Soc.. This book was released on 2011-08-10 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book establishes the basic function theory and complex geometry of Riemann surfaces, both open and compact. Many of the methods used in the book are adaptations and simplifications of methods from the theories of several complex variables and complex analytic geometry and would serve as excellent training for mathematicians wanting to work in complex analytic geometry. After three introductory chapters, the book embarks on its central, and certainly most novel, goal of studying Hermitian holomorphic line bundles and their sections. Among other things, finite-dimensionality of spaces of sections of holomorphic line bundles of compact Riemann surfaces and the triviality of holomorphic line bundles over Riemann surfaces are proved, with various applications. Perhaps the main result of the book is Hormander's Theorem on the square-integrable solution of the Cauchy-Riemann equations. The crowning application is the proof of the Kodaira and Narasimhan Embedding Theorems for compact and open Riemann surfaces. The intended reader has had first courses in real and complex analysis, as well as advanced calculus and basic differential topology (though the latter subject is not crucial). As such, the book should appeal to a broad portion of the mathematical and scientific community. This book is the first to give a textbook exposition of Riemann surface theory from the viewpoint of positive Hermitian line bundles and Hormander $\bar \partial$ estimates. It is more analytical and PDE oriented than prior texts in the field, and is an excellent introduction to the methods used currently in complex geometry, as exemplified in J. P. Demailly's online but otherwise unpublished book ``Complex analytic and differential geometry.'' I used it for a one quarter course on Riemann surfaces and found it to be clearly written and self-contained. It not only fills a significant gap in the large textbook literature on Riemann surfaces but is also rather indispensible for those who would like to teach the subject from a differential geometric and PDE viewpoint. --Steven Zelditch
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 and published by American Mathematical Soc.. This book was released on 2002 with total page 530 pages. 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.
