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Author: Raghavan Narasimhan
Publisher:
ISBN:
Category : Analytic spaces
Languages : en
Pages : 160
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Book Description
Author: Raghavan Narasimhan
Publisher:
ISBN:
Category : Analytic spaces
Languages : en
Pages : 160
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Book Description
Author: H. Grauert
Publisher: Springer Science & Business Media
ISBN: 3642695825
Category : Mathematics
Languages : en
Pages : 267
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Book Description
... 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
Author: Steven Bell
Publisher: Springer Science & Business Media
ISBN: 9783540629955
Category : Mathematics
Languages : en
Pages : 324
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Book Description
The articles in this volume were written to commemorate Reinhold Remmert's 60th birthday in June, 1990. They are surveys, meant to facilitate access to some of the many aspects of the theory of complex manifolds, and demonstrate the interplay between complex analysis and many other branches of mathematics, algebraic geometry, differential topology, representations of Lie groups, and mathematical physics being only the most obvious of these branches. Each of these articles should serve not only to describe the particular circle of ideas in complex analysis with which it deals but also as a guide to the many mathematical ideas related to its theme.
Author: H. Grauert
Publisher: Springer Science & Business Media
ISBN: 3662098733
Category : Mathematics
Languages : en
Pages : 374
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Book Description
The first survey of its kind, written by internationally known, outstanding experts who developed substantial parts of the field. The book contains an introduction written by Remmert, describing the history of the subject, and is very useful to graduate students and researchers in complex analysis, algebraic geometry and differential geometry.
Author: Jörg Eschmeier
Publisher: Oxford University Press
ISBN: 9780198536673
Category : Language Arts & Disciplines
Languages : en
Pages : 378
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Book Description
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.
Author: Esnault
Publisher: Birkhäuser
ISBN: 3034886004
Category : Science
Languages : en
Pages : 173
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Book Description
Introduction M. Kodaira's vanishing theorem, saying that the inverse of an ample invert ible sheaf on a projective complex manifold X has no cohomology below the dimension of X and its generalization, due to Y. Akizuki and S. Nakano, have been proven originally by methods from differential geometry ([39J and [1]). Even if, due to J.P. Serre's GAGA-theorems [56J and base change for field extensions the algebraic analogue was obtained for projective manifolds over a field k of characteristic p = 0, for a long time no algebraic proof was known and no generalization to p > 0, except for certain lower dimensional manifolds. Worse, counterexamples due to M. Raynaud [52J showed that in characteristic p > 0 some additional assumptions were needed. This was the state of the art until P. Deligne and 1. Illusie [12J proved the degeneration of the Hodge to de Rham spectral sequence for projective manifolds X defined over a field k of characteristic p > 0 and liftable to the second Witt vectors W2(k). Standard degeneration arguments allow to deduce the degeneration of the Hodge to de Rham spectral sequence in characteristic zero, as well, a re sult which again could only be obtained by analytic and differential geometric methods beforehand. As a corollary of their methods M. Raynaud (loc. cit.) gave an easy proof of Kodaira vanishing in all characteristics, provided that X lifts to W2(k).
Author: F. Gherardelli
Publisher: Springer Science & Business Media
ISBN: 3642109640
Category : Mathematics
Languages : en
Pages : 466
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Book Description
A. Andreotti: Nine lectures on complex analysis.- J.J. Kohn: Propagations of singularities for the Cauchy-Riemann equations.- Yum-Tong Siu: The mixed case of the direct image theorem and its applications.
Author: Barbara Fantechi
Publisher: American Mathematical Soc.
ISBN: 0821842455
Category : Mathematics
Languages : en
Pages : 354
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Book Description
Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.
Author: M. P. Fourman
Publisher: Springer
ISBN: 3540348492
Category : Mathematics
Languages : en
Pages : 798
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Book Description
Author: Ingrid Bauer
Publisher: Springer Science & Business Media
ISBN: 3642562027
Category : Mathematics
Languages : en
Pages : 357
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Book Description
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.
