Complex Analytic Desingularization
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Complex Analytic Desingularization
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Author : José Manuel Aroca
language : en
Publisher: Springer
Release Date : 2018-11-03
Complex Analytic Desingularization written by José Manuel Aroca and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-03 with Mathematics categories.
[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.
Desingularization Of A Complex Analytic Space
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Author : Heisuke Hironaka
language : en
Publisher:
Release Date :
Desingularization Of A Complex Analytic Space written by Heisuke Hironaka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Contributions To Complex Analysis And Analytic Geometry
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Author : Henri Skoda
language : de
Publisher: Springer-Verlag
Release Date : 2013-08-13
Contributions To Complex Analysis And Analytic Geometry written by Henri Skoda and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-13 with Mathematics categories.
Resolution Of Surface Singularities
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Author : Vincent Cossart
language : en
Publisher: Springer
Release Date : 2006-11-14
Resolution Of Surface Singularities written by Vincent Cossart 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.
Lectures On Analytic Differential Equations
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Author : I︠U︡. S. Ilʹi︠a︡shenko
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Lectures On Analytic Differential Equations written by I︠U︡. S. Ilʹi︠a︡shenko 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 2008 with Mathematics categories.
The book combines the features of a graduate-level textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. As a graduate textbook, it includes self-contained, sometimes considerably simplified demonstrations of several fundamental results, which previously appeared only in journal publications (desingularization of planar analytic vector fields, existence of analytic separatrices, positive and negative results on the Riemann-Hilbert problem, Ecalle-Voronin and Martinet-Ramis moduli, solution of the Poincare problem on the degree of an algebraic separatrix, etc.). As a research monograph, it explores in a systematic way the algebraic decidability of local classification problems, rigidity of holomorphic foliations, etc. Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the mor The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. on several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area.
Introduction To Real Analytic Sets And Real Analytic Maps
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Author : Heisuke Hironaka
language : en
Publisher:
Release Date : 1973
Introduction To Real Analytic Sets And Real Analytic Maps written by Heisuke Hironaka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Analytic mappings categories.
Multidimensional Complex Analysis And Partial Differential Equations
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Author : Francois Treves
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Multidimensional Complex Analysis And Partial Differential Equations written by Francois Treves 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 1997 with Mathematics categories.
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.
Analytic Partial Differential Equations
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Author : François Treves
language : en
Publisher: Springer Nature
Release Date : 2022-04-26
Analytic Partial Differential Equations written by François Treves and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-26 with Mathematics categories.
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.
Non Analytic Singular Continuations Of Complex Analytic Dynamical Systems
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Author : Brett David Bozyk
language : en
Publisher:
Release Date : 2012
Non Analytic Singular Continuations Of Complex Analytic Dynamical Systems written by Brett David Bozyk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
Complex Analysis
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Author : Peter Ebenfelt
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-30
Complex Analysis written by Peter Ebenfelt 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 2011-01-30 with Mathematics categories.
This volume presents the proceedings of a conference on Several Complex Variables, PDE’s, Geometry, and their interactions held in 2008 at the University of Fribourg, Switzerland, in honor of Linda Rothschild.