Local Analytic Geometry

Author : Theo de Jong
Publisher : Springer Science & Business Media
ISBN 13 : 3322901599
Total Pages : 395 pages
Book Rating : 4.90/5 ( download)

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Download or read book Local Analytic Geometry written by Theo de Jong and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Auf der Grundlage einer Einführung in die kommutative Algebra, algebraische Geometrie und komplexe Analysis werden zunächst Kurvensingularitäten untersucht. Daran schließen Ergebnisse an, die zum ersten Mal in einem Lehrbuch aufgenommen wurden, das Verhalten von Invarianten in Familien, Standardbasen für konvergente Potenzreihenringe, Approximationssätze, Grauerts Satz über die Existenz der versellen Deformation. Das Buch richtet sich an Studenten höherer Semester, Doktoranden und Dozenten. Es ist auf der Grundlage mehrerer Vorlesungen und Seminaren an den Universitäten in Kaiserslautern und Saarbrücken entstanden.

Author : Shreeram Shankar Abhyankar
Publisher : World Scientific
ISBN 13 : 981024505X
Total Pages : 506 pages
Book Rating : 4.54/5 ( download)

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Download or read book Local Analytic Geometry written by Shreeram Shankar Abhyankar and published by World Scientific. This book was released on 2001 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Stanislaw Lojasiewicz
Publisher : Birkhäuser
ISBN 13 : 3034876173
Total Pages : 535 pages
Book Rating : 4.79/5 ( download)

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Download or read book Introduction to Complex Analytic Geometry written by Stanislaw Lojasiewicz and published by Birkhäuser. This book was released on 2013-03-09 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: facts. An elementary acquaintance with topology, algebra, and analysis (in cluding the notion of a manifold) is sufficient as far as the understanding of this book is concerned. All the necessary properties and theorems have been gathered in the preliminary chapters -either with proofs or with references to standard and elementary textbooks. The first chapter of the book is devoted to a study of the rings Oa of holomorphic functions. The notions of analytic sets and germs are introduced in the second chapter. Its aim is to present elementary properties of these objects, also in connection with ideals of the rings Oa. The case of principal germs (§5) and one-dimensional germs (Puiseux theorem, §6) are treated separately. The main step towards understanding of the local structure of analytic sets is Ruckert's descriptive lemma proved in Chapter III. Among its conse quences is the important Hilbert Nullstellensatz (§4). In the fourth chapter, a study of local structure (normal triples, § 1) is followed by an exposition of the basic properties of analytic sets. The latter includes theorems on the set of singular points, irreducibility, and decom position into irreducible branches (§2). The role played by the ring 0 A of an analytic germ is shown (§4). Then, the Remmert-Stein theorem on re movable singularities is proved (§6). The last part of the chapter deals with analytically constructible sets (§7).

Author : Bruno Anglès
Publisher : Springer Nature
ISBN 13 : 3030662497
Total Pages : 337 pages
Book Rating : 4.93/5 ( download)

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Download or read book Arithmetic and Geometry over Local Fields written by Bruno Anglès and published by Springer Nature. This book was released on 2021-03-03 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces some recent developments in Arithmetic Geometry over local fields. Its seven chapters are centered around two common themes: the study of Drinfeld modules and non-Archimedean analytic geometry. The notes grew out of lectures held during the research program "Arithmetic and geometry of local and global fields" which took place at the Vietnam Institute of Advanced Study in Mathematics (VIASM) from June to August 2018. The authors, leading experts in the field, have put great effort into making the text as self-contained as possible, introducing the basic tools of the subject. The numerous concrete examples and suggested research problems will enable graduate students and young researchers to quickly reach the frontiers of this fascinating branch of mathematics.

Author : Vladimir G. Berkovich
Publisher : American Mathematical Soc.
ISBN 13 : 0821890204
Total Pages : 181 pages
Book Rating : 4.02/5 ( download)

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Download or read book Spectral Theory and Analytic Geometry over Non-Archimedean Fields written by Vladimir G. Berkovich and published by American Mathematical Soc.. This book was released on 2012-08-02 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to introduce a new notion of analytic space over a non-Archimedean field. Despite the total disconnectedness of the ground field, these analytic spaces have the usual topological properties of a complex analytic space, such as local compactness and local arcwise connectedness. This makes it possible to apply the usual notions of homotopy and singular homology. The book includes a homotopic characterization of the analytic spaces associated with certain classes of algebraic varieties and an interpretation of Bruhat-Tits buildings in terms of these analytic spaces. The author also studies the connection with the earlier notion of a rigid analytic space. Geometrical considerations are used to obtain some applications, and the analytic spaces are used to construct the foundations of a non-Archimedean spectral theory of bounded linear operators. This book requires a background at the level of basic graduate courses in algebra and topology, as well as some familiarity with algebraic geometry. It would be of interest to research mathematicians and graduate students working in algebraic geometry, number theory, and -adic analysis.

Author : Theo de Jong
Publisher : Vieweg+Teubner Verlag
ISBN 13 : 9783528031374
Total Pages : 384 pages
Book Rating : 4.79/5 ( download)

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Download or read book Local Analytic Geometry written by Theo de Jong and published by Vieweg+Teubner Verlag. This book was released on 2000-04-27 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Auf der Grundlage einer Einführung in die kommutative Algebra, algebraische Geometrie und komplexe Analysis werden zunächst Kurvensingularitäten untersucht. Daran schließen Ergebnisse an, die zum ersten Mal in einem Lehrbuch aufgenommen wurden, das Verhalten von Invarianten in Familien, Standardbasen für konvergente Potenzreihenringe, Approximationssätze, Grauerts Satz über die Existenz der versellen Deformation. Das Buch richtet sich an Studenten höherer Semester, Doktoranden und Dozenten. Es ist auf der Grundlage mehrerer Vorlesungen und Seminaren an den Universitäten in Kaiserslautern und Saarbrücken entstanden.

Author : Tatsuo Suwa
Publisher : World Scientific
ISBN 13 : 9814704296
Total Pages : 609 pages
Book Rating : 4.98/5 ( download)

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Download or read book Complex Analytic Geometry: From The Localization Viewpoint written by Tatsuo Suwa and published by World Scientific. This book was released on 2024-02-21 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Siegfried Bosch
Publisher : Springer
ISBN 13 : 3319044176
Total Pages : 254 pages
Book Rating : 4.70/5 ( download)

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Download or read book Lectures on Formal and Rigid Geometry written by Siegfried Bosch and published by Springer. This book was released on 2014-08-22 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".

Author : Jeffery D. McNeal
Publisher : American Mathematical Soc.
ISBN 13 : 0821872753
Total Pages : 601 pages
Book Rating : 4.58/5 ( download)

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Download or read book Analytic and Algebraic Geometry written by Jeffery D. McNeal and published by American Mathematical Soc.. This book was released on 2010-01-01 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Author : Gert-Martin Greuel
Publisher : Springer Science & Business Media
ISBN 13 : 3540284192
Total Pages : 482 pages
Book Rating : 4.92/5 ( download)

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Download or read book Introduction to Singularities and Deformations written by Gert-Martin Greuel and published by Springer Science & Business Media. This book was released on 2007-02-23 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.