Complex Analytic Desingularization

Author : José Manuel Aroca,Heisuke Hironaka,José Luis Vicente
Publisher : Springer
Page : 330 pages
File Size : 43,5 Mb
Release : 2018-11-03
Category : Mathematics
ISBN : 9784431498223

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Complex Analytic Desingularization by José Manuel Aroca,Heisuke Hironaka,José Luis Vicente Pdf

[From the foreword by B. Teissier] The main ideas of the proof of resolution of singularities of complex-analytic spaces presented here were developed by Heisuke Hironaka in the late 1960s and early 1970s. Since then, a number of proofs, all inspired by Hironaka's general approach, have appeared, the validity of some of them extending beyond the complex analytic case. The proof has now been so streamlined that, although it was seen 50 years ago as one of the most difficult proofs produced by mathematics, it can now be the subject of an advanced university course. Yet, far from being of historical interest only, this long-awaited book will be very rewarding for any mathematician interested in singularity theory. Rather than a proof of a canonical or algorithmic resolution of singularities, what is presented is in fact a masterly study of the infinitely near “worst” singular points of a complex analytic space obtained by successive “permissible” blowing ups and of the way to tame them using certain subspaces of the ambient space. This taming proves by an induction on the dimension that there exist finite sequences of permissible blowing ups at the end of which the worst infinitely near points have disappeared, and this is essentially enough to obtain resolution of singularities. Hironaka’s ideas for resolution of singularities appear here in a purified and geometric form, in part because of the need to overcome the globalization problems appearing in complex analytic geometry. In addition, the book contains an elegant presentation of all the prerequisites of complex analytic geometry, including basic definitions and theorems needed to follow the development of ideas and proofs. Its epilogue presents the use of similar ideas in the resolution of singularities of complex analytic foliations. This text will be particularly useful and interesting for readers of the younger generation who wish to understand one of the most fundamental results in algebraic and analytic geometry and invent possible extensions and applications of the methods created to prove it.

Author : Francois Treves,Paulo D. Cordaro,Howard Jacobowitz
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 53,7 Mb
Release : 1997
Category : Analyse fonctionnelle - Congrès
ISBN : 9780821805091

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Multidimensional Complex Analysis and Partial Differential Equations by Francois Treves,Paulo D. Cordaro,Howard Jacobowitz Pdf

This collection of papers by outstanding contributors in analysis, partial differential equations and several complex variables is dedicated to Professor Treves in honour of his 65th birthday. There are five excellent survey articles covering analytic singularities, holomorphically nondegenerate algebraic hypersurfaces, analyticity of CR mappings, removable singularities of vector fields and local solvability for systems of vector fields. The other papers are original research contributions on topics such as Klein-Gordon and Dirac equations, Toeplitz operators, elliptic structures, complexification of Lie groups, and pseudo-differential operators.

Author : François Treves
Publisher : Springer Nature
Page : 1221 pages
File Size : 52,9 Mb
Release : 2022-04-26
Category : Mathematics
ISBN : 9783030940553

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Analytic Partial Differential Equations by François Treves Pdf

This book provides a coherent, self-contained introduction to central topics of Analytic Partial Differential Equations in the natural geometric setting. The main themes are the analysis in phase-space of analytic PDEs and the Fourier–Bros–Iagolnitzer (FBI) transform of distributions and hyperfunctions, with application to existence and regularity questions. The book begins by establishing the fundamental properties of analytic partial differential equations, starting with the Cauchy–Kovalevskaya theorem, before presenting an integrated overview of the approach to hyperfunctions via analytic functionals, first in Euclidean space and, once the geometric background has been laid out, on analytic manifolds. Further topics include the proof of the Lojaciewicz inequality and the division of distributions by analytic functions, a detailed description of the Frobenius and Nagano foliations, and the Hamilton–Jacobi solutions of involutive systems of eikonal equations. The reader then enters the realm of microlocal analysis, through pseudodifferential calculus, introduced at a basic level, followed by Fourier integral operators, including those with complex phase-functions (à la Sjöstrand). This culminates in an in-depth discussion of the existence and regularity of (distribution or hyperfunction) solutions of analytic differential (and later, pseudodifferential) equations of principal type, exemplifying the usefulness of all the concepts and tools previously introduced. The final three chapters touch on the possible extension of the results to systems of over- (or under-) determined systems of these equations—a cornucopia of open problems. This book provides a unified presentation of a wealth of material that was previously restricted to research articles. In contrast to existing monographs, the approach of the book is analytic rather than algebraic, and tools such as sheaf cohomology, stratification theory of analytic varieties and symplectic geometry are used sparingly and introduced as required. The first half of the book is mainly pedagogical in intent, accessible to advanced graduate students and postdocs, while the second, more specialized part is intended as a reference for researchers.

Author : Andrew J Sommese,Charles W Wampler, Ii
Publisher : World Scientific
Page : 425 pages
File Size : 40,5 Mb
Release : 2005-03-21
Category : Mathematics
ISBN : 9789814480888

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The Numerical Solution Of Systems Of Polynomials Arising In Engineering And Science by Andrew J Sommese,Charles W Wampler, Ii Pdf

Written by the founders of the new and expanding field of numerical algebraic geometry, this is the first book that uses an algebraic-geometric approach to the numerical solution of polynomial systems and also the first one to treat numerical methods for finding positive dimensional solution sets. The text covers the full theory from methods developed for isolated solutions in the 1980's to the most recent research on positive dimensional sets.

Author : Anonim
Publisher : Unknown
Page : 1008 pages
File Size : 50,6 Mb
Release : 1971
Category : Geometry
ISBN : CORNELL:31924001555667

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Actes du congrès international des mathématiciens, 1970 by Anonim Pdf

Author : Henri Skoda,Jean-Marie Trépreau
Publisher : Springer-Verlag
Page : 261 pages
File Size : 47,8 Mb
Release : 2013-08-13
Category : Mathematics
ISBN : 9783663141969

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Contributions to Complex Analysis and Analytic Geometry by Henri Skoda,Jean-Marie Trépreau Pdf

Author : H. Grauert,Thomas Peternell,R. Remmert
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 47,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662098738

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Several Complex Variables VII by H. Grauert,Thomas Peternell,R. Remmert Pdf

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 : Oscar Blasco
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 47,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821852750

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Topics in Complex Analysis and Operator Theory by Oscar Blasco Pdf

This book contains the lecture notes as well as some invited papers presented at the Third Winter School in Complex Analysis, Operator Theory and Applications held February 2-5, 2010, in Valencia, Spain. The book is divided into two parts. The first is an extended self-contained version of the mini-courses taught at the School. The papers in this first part are: Notes on real analytic functions and classical operators, by Pawel Domanski; Shining a Hilbertian lamp on the bidisk, by John E. McCarthy; Selected problems in perturbation theory, by Vladimir V. Peller; and Composition operators on Hardy-Orlicz spaces, by Luis Rodriguez-Piazza. The second part consists of several research papers on recent advances in the area and some survey articles of an expository character. The articles in this second part are: Remarks on weighted mixed norm spaces, by O. Blasco; Interpolation subspaces of $L^1$ of a vector measure and norm inequalities for the integration operator, by J.M. Calabuig, J. Rodriguez, and E.A. Sanchez-Perez; On the spectra of algebras of analytic functions, by D. Carando, D. Garcia, M. Maestre, and P. Sevilla-Peris; Holomorphic self-maps of the disk intertwining two linear fractional maps, by M.D. Contreras, S. Diaz-Madrigal, M.J. Martin, and D. Vukotic; ABC-type estimates via Garsia-type norms, by K.M. Dyakonov; and Volterra type operators on Bergman spaces with exponential weights, by J. Pau and J.A. Pelaez. The topics selected for the mini-courses cover several aspects of complex analysis and operator theory that play important roles in understanding connections between different areas that are considered in fashion these days. This part is aimed at graduate students and young researchers. The courses are self-contained, focusing on those aspects that are basic and that can lead the readers to a quick understanding of the theories presented in each topic. They start with the classical results and reach a selection of open problems in each case. The research and survey articles are aimed at young researchers in the area, as well as post-doc and senior researchers interested in complex analysis and operator theory. This book is published in cooperation with Real Sociedad Matematica Espanola.

Author : Felipe Cano
Publisher : Springer Nature
Page : 531 pages
File Size : 44,7 Mb
Release : 2024-06-18
Category : Electronic
ISBN : 9783031524813

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Handbook of Geometry and Topology of Singularities V: Foliations by Felipe Cano Pdf

Author : José Luis Cisneros-Molina,Lê Dũng Tráng,José Seade
Publisher : Springer Nature
Page : 622 pages
File Size : 49,7 Mb
Release : 2023-11-10
Category : Mathematics
ISBN : 9783031319259

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Handbook of Geometry and Topology of Singularities IV by José Luis Cisneros-Molina,Lê Dũng Tráng,José Seade Pdf

This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex. Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Author : Vincent Cossart,Jean Giraud,Ulrich Orbanz
Publisher : Springer
Page : 138 pages
File Size : 49,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540391258

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Resolution of Surface Singularities by Vincent Cossart,Jean Giraud,Ulrich Orbanz Pdf

Author : J Noguchi,Hirotaka Fujimoto,J Kajiwara,Takeo Ohsawa
Publisher : World Scientific
Page : 738 pages
File Size : 46,8 Mb
Release : 1996-05-09
Category : Electronic
ISBN : 9789814548595

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Geometric Complex Analysis - Proceedings Of The Third International Research Institute Of Mathematical Society Of Japan by J Noguchi,Hirotaka Fujimoto,J Kajiwara,Takeo Ohsawa Pdf

This proceedings is a collection of articles in several complex variables with emphasis on geometric methods and results, which includes several survey papers reviewing the development of the topics in these decades. Through this volume one can see an active field providing insight into other fields like algebraic geometry, dynamical systems and partial differential equations.

Author : José Luis Cisneros Molina,Dũng Tráng Lê,José Seade
Publisher : Springer Nature
Page : 616 pages
File Size : 54,6 Mb
Release : 2020-10-24
Category : Mathematics
ISBN : 9783030530617

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Handbook of Geometry and Topology of Singularities I by José Luis Cisneros Molina,Dũng Tráng Lê,José Seade Pdf

This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject. This is the first volume in a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Author : Denis Cheniot,Jean-Paul Brasselet
Publisher : World Scientific
Page : 1083 pages
File Size : 46,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812707499

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Singularity Theory by Denis Cheniot,Jean-Paul Brasselet Pdf

The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory. The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 40,8 Mb
Release : 2024-06-18
Category : Electronic
ISBN : 9789814476393

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Singularity Theory by Anonim Pdf