Full Holomorphic Maps from the Riemann Sphere to Complex Projective Space
Author : Thomas Arleigh Crawford
Publisher :
Page : 108 pages
File Size : 25,89 MB
Release : 1992
Category : Holomorphic mappings
ISBN :
Author : Thomas Arleigh Crawford
Publisher :
Page : 108 pages
File Size : 25,89 MB
Release : 1992
Category : Holomorphic mappings
ISBN :
Author : John W. Havlicek
Publisher :
Page : 278 pages
File Size : 35,46 MB
Release : 1992
Category :
ISBN :
Author : Rick Miranda
Publisher : American Mathematical Soc.
Page : 414 pages
File Size : 23,98 MB
Release : 1995
Category : Mathematics
ISBN : 0821802682
In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking centre stage. But the main examples come fromprojective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Dualtiy Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves andcohomology are introduced as a unifying device in the later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.
Author : Katsumi Nomizu
Publisher : American Mathematical Soc.
Page : 160 pages
File Size : 32,30 MB
Release : 1997
Category : Mathematics
ISBN : 9780821808405
The five papers originally appeared in Japanese in the journal Sugaku and would ordinarily appear in the Society's translation of that journal, but are published separately here to expedite their dissemination. They explore such aspects as representation theory, differential geometry, invariant theory, and complex analysis. No index. Member prices are $47 for institutions and $35 for individual. Annotation copyrighted by Book News, Inc., Portland, OR.
Author : Jeremy Kenneth Miller
Publisher :
Page : pages
File Size : 48,10 MB
Release : 2012
Category :
ISBN :
In [Seg79], Graeme Segal proved that the space of holomorphic maps from a Riemann surface to a complex projective space is homology equivalent to the corresponding continuous mapping space through a range of dimensions increasing with degree. I will address if a similar result holds when other almost complex structures are put on projective space. For any compatible almost complex structure J on CP^2, I prove that the inclusion map from the space of J-holomorphic maps to the space of continuous maps induces a homology surjection through a range of dimensions tending to infinity with degree. The proof involves comparing the scanning map of topological chiral homology ([Sal01], [Lur09], [And10]) with gluing of J-holomorphic curves ([MS94], [Sik03]).
Author : Jacques Hurtubise
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 28,75 MB
Release : 1997-03-31
Category : Mathematics
ISBN : 9780792345008
Gauge theory, symplectic geometry and symplectic topology are important areas at the crossroads of several mathematical disciplines. The present book, with expertly written surveys of recent developments in these areas, includes some of the first expository material of Seiberg-Witten theory, which has revolutionised the subjects since its introduction in late 1994. Topics covered include: introductions to Seiberg-Witten theory, to applications of the S-W theory to four-dimensional manifold topology, and to the classification of symplectic manifolds; an introduction to the theory of pseudo-holomorphic curves and to quantum cohomology; algebraically integrable Hamiltonian systems and moduli spaces; the stable topology of gauge theory, Morse-Floer theory; pseudo-convexity and its relations to symplectic geometry; generating functions; Frobenius manifolds and topological quantum field theory.
Author : Benson Farb
Publisher : American Mathematical Soc.
Page : 371 pages
File Size : 44,35 MB
Release : 2013-08-16
Category : Mathematics
ISBN : 0821898876
Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Author : T. Arleigh Crawford
Publisher :
Page : 14 pages
File Size : 49,9 MB
Release : 1993
Category :
ISBN :
Author : R. Narasimhan
Publisher : Birkhäuser
Page : 127 pages
File Size : 46,84 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3034886179
Author : Klaus Fritzsche
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 24,21 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 146849273X
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.