The Monodromy Groups Of Isolated Singularities Of Complete Intersections
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The Monodromy Groups Of Isolated Singularities Of Complete Intersections
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Author : Wolfgang Ebeling
language : en
Publisher: Springer
Release Date : 1987-12-09
The Monodromy Groups Of Isolated Singularities Of Complete Intersections written by Wolfgang Ebeling and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-12-09 with Mathematics categories.
Singularities
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Author : Vladimir I. Arnold
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Singularities written by Vladimir I. Arnold and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In July 1996, a conference was organized by the editors of this volume at the Mathematische Forschungsinstitut Oberwolfach to honour Egbert Brieskorn on the occasion of his 60th birthday. Most of the mathematicians invited to the conference have been influenced in one way or another by Brieskorn's work in singularity theory. It was the first time that so many people from the Russian school could be present at a conference in singularity theory outside Russia. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrating the breadth of Brieskorn's own interests. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrates the breadth of Brieskorn's own interests.
Isolated Singular Points On Complete Intersections
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Author : Eduard Looijenga
language : en
Publisher: Cambridge University Press
Release Date : 1984-03
Isolated Singular Points On Complete Intersections written by Eduard Looijenga and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-03 with Mathematics categories.
This book will be of use to professional mathematicians working in algebraic geometry, complex-analytical geometry and, to some extent, differential analysis.
Handbook Of Geometry And Topology Of Singularities I
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Author : José Luis Cisneros Molina
language : en
Publisher: Springer Nature
Release Date : 2020-10-24
Handbook Of Geometry And Topology Of Singularities I written by José Luis Cisneros Molina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-24 with Mathematics categories.
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.
Applied Picard Lefschetz Theory
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Author : V. A. Vasilʹev
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Applied Picard Lefschetz Theory written by V. A. Vasilʹev 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 2002 with Mathematics categories.
Many important functions of mathematical physics are defined as integrals depending on parameters. The Picard-Lefschetz theory studies how analytic and qualitative properties of such integrals (regularity, algebraicity, ramification, singular points, etc.) depend on the monodromy of corresponding integration cycles. In this book, V. A. Vassiliev presents several versions of the Picard-Lefschetz theory, including the classical local monodromy theory of singularities and completeintersections, Pham's generalized Picard-Lefschetz formulas, stratified Picard-Lefschetz theory, and also twisted versions of all these theories with applications to integrals of multivalued forms. The author also shows how these versions of the Picard-Lefschetz theory are used in studying a variety ofproblems arising in many areas of mathematics and mathematical physics. In particular, he discusses the following classes of functions: volume functions arising in the Archimedes-Newton problem of integrable bodies; Newton-Coulomb potentials; fundamental solutions of hyperbolic partial differential equations; multidimensional hypergeometric functions generalizing the classical Gauss hypergeometric integral. The book is geared toward a broad audience of graduate students, research mathematiciansand mathematical physicists interested in algebraic geometry, complex analysis, singularity theory, asymptotic methods, potential theory, and hyperbolic operators.
On The Topology Of Isolated Singularities In Analytic Spaces
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Author : José Seade
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-21
On The Topology Of Isolated Singularities In Analytic Spaces written by José Seade 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 2006-03-21 with Mathematics categories.
Offers an overview of selected topics on the topology of singularities, with emphasis on its relations to other branches of geometry and topology. This book studies real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations.
Ramified Integrals Singularities And Lacunas
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Author : V.A. Vassiliev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Ramified Integrals Singularities And Lacunas written by V.A. Vassiliev 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 2012-12-06 with Mathematics categories.
Solutions to many problems of these theories are treated. Subjects include the proof of multidimensional analogues of Newton's theorem on the nonintegrability of ovals; extension of the proofs for the theorems of Newton, Ivory, Arnold and Givental on potentials of algebraic surfaces. Also, it is discovered for which d and n the potentials of degree d hyperbolic surfaces in [actual symbol not reproducible] are algebraic outside the surfaces; the equivalence of local regularity (the so-called sharpness), of fundamental solutions of hyperbolic PDEs and the topological Petrovskii-Atiyah-Bott-Garding condition is proved, and the geometrical characterization of domains of sharpness close to simple singularities of wave fronts is considered; a 'stratified' version of the Picard-Lefschetz formula is proved, and an algorithm enumerating topologically distinct Morsifications of real function singularities is given.
Dynamical Systems Viii
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Author : V.I. Arnol'd
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Dynamical Systems Viii written by V.I. Arnol'd 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 2013-03-09 with Mathematics categories.
In the first volume of this survey (Arnol'd et al. (1988), hereafter cited as "EMS 6") we acquainted the reader with the basic concepts and methods of the theory of singularities of smooth mappings and functions. This theory has numerous applications in mathematics and physics; here we begin describing these applica tions. Nevertheless the present volume is essentially independent of the first one: all of the concepts of singularity theory that we use are introduced in the course of the presentation, and references to EMS 6 are confined to the citation of technical results. Although our main goal is the presentation of analready formulated theory, the readerwill also come upon some comparatively recent results, apparently unknown even to specialists. We pointout some of these results. 2 3 In the consideration of mappings from C into C in§ 3. 6 of Chapter 1, we define the bifurcation diagram of such a mapping, formulate a K(n, 1)-theorem for the complements to the bifurcation diagrams of simple singularities, give the definition of the Mond invariant N in the spirit of "hunting for invariants", and we draw the reader's attention to a method of constructing the image of a mapping from the corresponding function on a manifold with boundary. In§ 4. 6 of the same chapter we introduce the concept of a versal deformation of a function with a nonisolated singularity in the dass of functions whose critical sets are arbitrary complete intersections of fixed dimension.
Singularities And Topology Of Hypersurfaces
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Author : Alexandru Dimca
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singularities And Topology Of Hypersurfaces written by Alexandru Dimca 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 2012-12-06 with Mathematics categories.
The Monodromy Group
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Author : Henryk Żołądek
language : en
Publisher: Springer Nature
Release Date : 2025-05-10
The Monodromy Group written by Henryk Żołądek and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-10 with Mathematics categories.
This book presents the monodromy group, underlining the unifying role it plays in a variety of theories and mathematical areas. In singularity theory and algebraic geometry, the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem and in mixed Hodge structures. In the theory of systems of linear differential equations, one has the Riemann-Hilbert problem, the Stokes phenomena and the hypergeometric functions with their multidimensional generalizations. In the theory of homomorphic foliations, there appear the Ecalle-Voronin-Martinet-Ramis moduli. Moreover, there is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions. The material is addressed to a wide audience, ranging from specialists in the theory of ordinary differential equations to algebraic geometers. Readers will quickly get introduced to modern and vital mathematical theories, such as singularity theory, analytic theory of ordinary differential equations, holomorphic foliations, Galois theory, and parts of algebraic geometry, without searching in vast literature. This second edition has been enlarged by several sections, presenting new results appeared since the first edition.