Coherent Analytic Sheaves
Title | Coherent Analytic Sheaves PDF eBook |
Author | H. Grauert |
Publisher | Springer Science & Business Media |
Pages | 267 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3642695825 |
... Je mehr ich tiber die Principien der Functionentheorie nachdenke - und ich thue dies unablassig -, urn so fester wird meine Uberzeugung, dass diese auf dem Fundamente algebraischer Wahrheiten aufgebaut werden muss (WEIERSTRASS, Glaubensbekenntnis 1875, Math. Werke II, p. 235). 1. Sheaf Theory is a general tool for handling questions which involve local solutions and global patching. "La notion de faisceau s'introduit parce qu'il s'agit de passer de donnees 'locales' a l'etude de proprietes 'globales'" [CAR], p. 622. The methods of sheaf theory are algebraic. The notion of a sheaf was first introduced in 1946 by J. LERAY in a short note Eanneau d'homologie d'une representation, C.R. Acad. Sci. 222, 1366-68. Of course sheaves had occurred implicitly much earlier in mathematics. The "Monogene analytische Functionen", which K. WEIERSTRASS glued together from "Func tionselemente durch analytische Fortsetzung", are simply the connected components of the sheaf of germs of holomorphic functions on a RIEMANN surface*'; and the "ideaux de domaines indetermines", basic in the work of K. OKA since 1948 (cf. [OKA], p. 84, 107), are just sheaves of ideals of germs of holomorphic functions. Highly original contributions to mathematics are usually not appreciated at first. Fortunately H. CARTAN immediately realized the great importance of LERAY'S new abstract concept of a sheaf. In the polycopied notes of his Semina ire at the E.N.S
Spectral Decompositions and Analytic Sheaves
Title | Spectral Decompositions and Analytic Sheaves PDF eBook |
Author | Jörg Eschmeier |
Publisher | Oxford University Press |
Pages | 378 |
Release | 1996 |
Genre | Language Arts & Disciplines |
ISBN | 9780198536673 |
Rapid developments in multivariable spectral theory have led to important and fascinating results which also have applications in other mathematical disciplines. In this book, various concepts from function theory and complex analytic geometry are drawn together to give a new approach to concrete spectral computations and give insights into new developments in the spectral theory of linear operators. Classical results from cohomology theory of Banach algebras, multidimensional spectral theory, and complex analytic geometry have been freshly interpreted using the language of homological algebra. The advantages of this approach are illustrated by a variety of examples, unexpected applications, and conceptually new ideas that should stimulate further research among mathematicians.
Gap-Sheaves and Extension of Coherent Analytic Subsheaves
Title | Gap-Sheaves and Extension of Coherent Analytic Subsheaves PDF eBook |
Author | Yum-Tong Siu |
Publisher | Springer |
Pages | 178 |
Release | 2006-11-15 |
Genre | Mathematics |
ISBN | 3540364293 |
The Geometry of Moduli Spaces of Sheaves
Title | The Geometry of Moduli Spaces of Sheaves PDF eBook |
Author | Daniel Huybrechts |
Publisher | Cambridge University Press |
Pages | 345 |
Release | 2010-05-27 |
Genre | Mathematics |
ISBN | 1139485822 |
This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
Algebraic and Analytic Geometry
Title | Algebraic and Analytic Geometry PDF eBook |
Author | Amnon Neeman |
Publisher | Cambridge University Press |
Pages | 433 |
Release | 2007-09-13 |
Genre | Mathematics |
ISBN | 0521709830 |
Modern introduction to algebraic geometry for undergraduates; uses analytic ideas to access algebraic theory.
Sheaves on Manifolds
Title | Sheaves on Manifolds PDF eBook |
Author | Masaki Kashiwara |
Publisher | Springer Science & Business Media |
Pages | 522 |
Release | 2013-03-14 |
Genre | Mathematics |
ISBN | 3662026619 |
Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view. From the reviews: "Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." –Bulletin of the L.M.S.
Theory of Stein Spaces
Title | Theory of Stein Spaces PDF eBook |
Author | H. Grauert |
Publisher | Springer Science & Business Media |
Pages | 269 |
Release | 2013-03-14 |
Genre | Mathematics |
ISBN | 1475743572 |
1. The classical theorem of Mittag-Leffler was generalized to the case of several complex variables by Cousin in 1895. In its one variable version this says that, if one prescribes the principal parts of a merom orphic function on a domain in the complex plane e, then there exists a meromorphic function defined on that domain having exactly those principal parts. Cousin and subsequent authors could only prove the analogous theorem in several variables for certain types of domains (e. g. product domains where each factor is a domain in the complex plane). In fact it turned out that this problem can not be solved on an arbitrary domain in em, m ~ 2. The best known example for this is a "notched" bicylinder in 2 2 e . This is obtained by removing the set { (z , z ) E e 11 z I ~ !, I z 1 ~ !}, from 1 2 1 2 2 the unit bicylinder, ~ :={(z , z ) E e llz1