Real Analytic And Algebraic Geometry
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Real Analytic And Algebraic Geometry
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Author : Margherita Galbiati
language : en
Publisher:
Release Date : 2014-01-15
Real Analytic And Algebraic Geometry written by Margherita Galbiati and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Real Analytic And Algebraic Geometry
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Author :
language : en
Publisher:
Release Date : 1990
Real Analytic And Algebraic Geometry written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Real Analytic And Algebraic Geometry
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Author : Margherita Galbiati
language : en
Publisher: Springer
Release Date : 2006-11-14
Real Analytic And Algebraic Geometry written by Margherita Galbiati and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Local Analytic Geometry
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Author : Shreeram Shankar Abhyankar
language : en
Publisher: World Scientific
Release Date : 2001
Local Analytic Geometry written by Shreeram Shankar Abhyankar and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory.The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from number theory. When it is specialized to the complex case, connectivity and other topological properties come to the fore. In particular, via singularities of analytic sets, topological fundamental groups can be studied.In the transition from punctual to local, i.e. from properties at a point to properties near a point, the classical work of Osgood plays an important role. This gives rise to normic forms and the concept of the Osgoodian. Following Serre, the passage from local to global properties of analytic spaces is facilitated by introducing sheaf theory. Here the fundamental results are the coherence theorems of Oka and Cartan. They are followed by theory normalization due to Oka and Zariski in the analytic and algebraic cases, respectively.
A Primer Of Real Analytic Functions
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Author : KRANTZ
language : en
Publisher: Birkhäuser
Release Date : 2013-03-09
A Primer Of Real Analytic Functions written by KRANTZ and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
The subject of real analytic functions is one of the oldest in mathe matical analysis. Today it is encountered early in ones mathematical training: the first taste usually comes in calculus. While most work ing mathematicians use real analytic functions from time to time in their work, the vast lore of real analytic functions remains obscure and buried in the literature. It is remarkable that the most accessible treatment of Puiseux's theorem is in Lefschetz's quite old Algebraic Geometry, that the clearest discussion of resolution of singularities for real analytic manifolds is in a book review by Michael Atiyah, that there is no comprehensive discussion in print of the embedding prob lem for real analytic manifolds. We have had occasion in our collaborative research to become ac quainted with both the history and the scope of the theory of real analytic functions. It seems both appropriate and timely for us to gather together this information in a single volume. The material presented here is of three kinds. The elementary topics, covered in Chapter 1, are presented in great detail. Even results like a real ana lytic inverse function theorem are difficult to find in the literature, and we take pains here to present such topics carefully. Topics of middling difficulty, such as separate real analyticity, Puiseux series, the FBI transform, and related ideas (Chapters 2-4), are covered thoroughly but rather more briskly.
Topics In Global Real Analytic Geometry
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Author : Francesca Acquistapace
language : en
Publisher: Springer Nature
Release Date : 2022-06-07
Topics In Global Real Analytic Geometry written by Francesca Acquistapace and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-07 with Mathematics categories.
In the first two chapters we review the theory developped by Cartan, Whitney and Tognoli. Then Nullstellensatz is proved both for Stein algebras and for the algebra of real analytic functions on a C-analytic space. Here we find a relation between real Nullstellensatz and seventeenth Hilbert’s problem for positive semidefinite analytic functions. Namely, a positive answer to Hilbert’s problem implies a solution for the real Nullstellensatz more similar to the one for real polinomials. A chapter is devoted to the state of the art on this problem that is far from a complete answer. In the last chapter we deal with inequalities. We describe a class of semianalytic sets defined by countably many global real analytic functions that is stable under topological properties and under proper holomorphic maps between Stein spaces, that is, verifies a direct image theorem. A smaller class admits also a decomposition into irreducible components as it happens for semialgebraic sets. During the redaction some proofs have been simplified with respect to the original ones.
Real Analytic And Algebraic Geometry
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Author : Fabrizio Broglia
language : en
Publisher: Walter de Gruyter
Release Date : 2011-07-11
Real Analytic And Algebraic Geometry written by Fabrizio Broglia and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-11 with Mathematics categories.
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Real Analytic And Algebraic Geometry
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Author :
language : en
Publisher:
Release Date : 1992
Real Analytic And Algebraic Geometry written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Geometry, Algebraic categories.
Lecture Notes On O Minimal Structures And Real Analytic Geometry
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Author : Chris Miller
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-14
Lecture Notes On O Minimal Structures And Real Analytic Geometry written by Chris Miller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-14 with Mathematics categories.
This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o-minimality and Hardy fields; Jean-Philippe Rolin on the construction of o-minimal structures from quasianalytic classes; Fernando Sanz on non-oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is an adaptation to the nonstandard setting of A.J. Wilkie's construction of o-minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such as research papers, conference proceedings and PhD theses. This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o-minimal structures by solutions, or images thereof, of definable systems of differential equations.
Analytic And Algebraic Geometry
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Author : Jeffery D. McNeal
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-01-01
Analytic And Algebraic Geometry written by Jeffery D. McNeal and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Mathematics categories.
"Analytic and algebraic geometers often study the same geometric structures but bring different methods to bear on them. While this dual approach has been spectacularly successful at solving problems, the language differences between algebra and analysis also represent a difficulty for students and researchers in geometry, particularly complex geometry. The PCMI program was designed to partially address this language gulf, by presenting some of the active developments in algebraic and analytic geometry in a form suitable for students on the 'other side' of the analysis-algebra language divide. One focal point of the summer school was multiplier ideals, a subject of wide current interest in both subjects. The present volume is based on a series of lectures at the PCMI summer school on analytic and algebraic geometry. The series is designed to give a high-level introduction to the advanced techniques behind some recent developments in algebraic and analytic geometry. The lectures contain many illustrative examples, detailed computations, and new perspectives on the topics presented, in order to enhance access of this material to non-specialists."--Publisher's description.