Topics In Global Real Analytic Geometry
DOWNLOAD
Download Topics In Global Real Analytic Geometry PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Topics In Global Real Analytic Geometry book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Topics In Global Real Analytic Geometry
DOWNLOAD
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.
Local Analytic Geometry
DOWNLOAD
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.
Recent Topics In Differential And Analytic Geometry
DOWNLOAD
Author : T. Ochiai
language : en
Publisher: Academic Press
Release Date : 2014-07-14
Recent Topics In Differential And Analytic Geometry written by T. Ochiai and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
Advanced Studies in Pure Mathematics, Volume 18-I: Recent Topics in Differential and Analytic Geometry presents the developments in the field of analytical and differential geometry. This book provides some generalities about bounded symmetric domains. Organized into two parts encompassing 12 chapters, this volume begins with an overview of harmonic mappings and holomorphic foliations. This text then discusses the global structures of a compact Kähler manifold that is locally decomposable as an isometric product of Ricci-positive, Ricci-negative, and Ricci-flat parts. Other chapters consider the most recognized non-standard examples of compact homogeneous Einstein manifolds constructed via Riemannian submersions. This book discusses as well the natural compactification of the moduli space of polarized Einstein–Kähler orbitfold with a given Hilbert polynomials. The final chapter deals with solving a degenerate Monge–Ampère equation by constructing a family of Einstein–Kähler metrics on the smooth part of minimal varieties of general kind. This book is a valuable resource for graduate students and pure mathematicians.
Real Analytic And Algebraic Geometry
DOWNLOAD
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.
Lecture Notes On O Minimal Structures And Real Analytic Geometry
DOWNLOAD
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.
Real Analytic And Algebraic Geometry
DOWNLOAD
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.
Complex Analytic Geometry From The Localization Viewpoint
DOWNLOAD
Author : Tatsuo Suwa
language : en
Publisher: World Scientific
Release Date : 2024-02-21
Complex Analytic Geometry From The Localization Viewpoint written by Tatsuo Suwa and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-21 with Mathematics categories.
Complex Analytic Geometry is a subject that could be termed, in short, as the study of the sets of common zeros of complex analytic functions. It has a long history and is closely related to many other fields of Mathematics and Sciences, where numerous applications have been found, including a recent one in the Sato hyperfunction theory.This book is concerned with, among others, local invariants that arise naturally in Complex Analytic Geometry and their relations with global invariants of the manifold or variety. The idea is to look at them as residues associated with the localization of some characteristic classes. Two approaches are taken for this — topological and differential geometric — and the combination of the two brings out further fruitful results. For this, on one hand, we present detailed description of the Alexander duality in combinatorial topology. On the other hand, we give a thorough presentation of the Čech-de Rham cohomology and integration theory on it. This viewpoint provides us with the way for clearer and more precise presentations of the central concepts as well as fundamental and important results that have been treated only globally so far. It also brings new perspectives into the subject and leads to further results and applications.The book starts off with basic material and continues by introducing characteristic classes via both the obstruction theory and the Chern-Weil theory, explaining the idea of localization of characteristic classes and presenting the aforementioned invariants and relations in a unified way from this perspective. Various related topics are also discussed. The expositions are carried out in a self-containing manner and includes recent developments. The profound consequences of this subject will make the book useful for students and researchers in fields as diverse as Algebraic Geometry, Complex Analytic Geometry, Differential Geometry, Topology, Singularity Theory, Complex Dynamical Systems, Algebraic Analysis and Mathematical Physics.
Analytic And Algebraic Geometry
DOWNLOAD
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.
Topics In Algebraic And Analytic Geometry Mn 13 Volume 13
DOWNLOAD
Author : Phillip A. Griffiths
language : en
Publisher: Princeton University Press
Release Date : 2015-03-08
Topics In Algebraic And Analytic Geometry Mn 13 Volume 13 written by Phillip A. Griffiths and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-08 with Mathematics categories.
This volume offers a systematic treatment of certain basic parts of algebraic geometry, presented from the analytic and algebraic points of view. The notes focus on comparison theorems between the algebraic, analytic, and continuous categories. Contents include: 1.1 sheaf theory, ringed spaces; 1.2 local structure of analytic and algebraic sets; 1.3 Pn 2.1 sheaves of modules; 2.2 vector bundles; 2.3 sheaf cohomology and computations on Pn; 3.1 maximum principle and Schwarz lemma on analytic spaces; 3.2 Siegel's theorem; 3.3 Chow's theorem; 4.1 GAGA; 5.1 line bundles, divisors, and maps to Pn; 5.2 Grassmanians and vector bundles; 5.3 Chern classes and curvature; 5.4 analytic cocycles; 6.1 K-theory and Bott periodicity; 6.2 K-theory as a generalized cohomology theory; 7.1 the Chern character and obstruction theory; 7.2 the Atiyah-Hirzebruch spectral sequence; 7.3 K-theory on algebraic varieties; 8.1 Stein manifold theory; 8.2 holomorphic vector bundles on polydisks; 9.1 concluding remarks; bibliography. Originally published in 1974. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Advanced Analytic Geometry
DOWNLOAD
Author : Alan Ditchfield Campbell
language : en
Publisher:
Release Date : 1938
Advanced Analytic Geometry written by Alan Ditchfield Campbell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1938 with Geometry, Analytic categories.