Coherent Analytic Sheaves

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

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... 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

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

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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

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

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Algebraic and Analytic 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

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Modern introduction to algebraic geometry for undergraduates; uses analytic ideas to access algebraic theory.

The Geometry of Moduli Spaces of Sheaves

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

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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.

Sheaves on Manifolds

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

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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.

Cohomology of Sheaves

Cohomology of Sheaves
Title Cohomology of Sheaves PDF eBook
Author Birger Iversen
Publisher Springer Science & Business Media
Pages 476
Release 2012-12-06
Genre Mathematics
ISBN 3642827837

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This text exposes the basic features of cohomology of sheaves and its applications. The general theory of sheaves is very limited and no essential result is obtainable without turn ing to particular classes of topological spaces. The most satis factory general class is that of locally compact spaces and it is the study of such spaces which occupies the central part of this text. The fundamental concepts in the study of locally compact spaces is cohomology with compact support and a particular class of sheaves,the so-called soft sheaves. This class plays a double role as the basic vehicle for the internal theory and is the key to applications in analysis. The basic example of a soft sheaf is the sheaf of smooth functions on ~n or more generally on any smooth manifold. A rather large effort has been made to demon strate the relevance of sheaf theory in even the most elementary analysis. This process has been reversed in order to base the fundamental calculations in sheaf theory on elementary analysis.