• Mathematics

Introduction to Singularities and Deformations


Author: Gert-Martin Greuel,Christoph Lossen,Eugenii I. Shustin
Publisher: Springer Science & Business Media
ISBN: 3540284192
Category: Mathematics
Page: 472
View: 2170
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.

    • Mathematics

Topology of Algebraic Varieties and Singularities

Conference in Honor of Anatoly Libgober's 60th Birthday, June 22-26, 2009, Jaca, Huesca, Spain
Author: Anatoly Libgober
Publisher: American Mathematical Soc.
ISBN: 0821848909
Category: Mathematics
Page: 467
View: 1407
This volume contains invited expository and research papers from the conference Topology of Algebraic Varieties, in honor of Anatoly Libgober's 60th birthday, held June 22-26, 2009, in Jaca, Spain. The volume contains four parts corresponding to the four main focal points of the conference: algebraic geometry and fundamental groups, braids and knots, hyperplane arrangements, and singularities. Together, the papers provide an overview of the current status of a broad range of topological questions in Algebraic Geometry.

    • Mathematics

Singular Points of Complex Hypersurfaces


Author: John Willard Milnor
Publisher: Princeton University Press
ISBN: 9780691080659
Category: Mathematics
Page: 122
View: 5332
The description for this book, Singular Points of Complex Hypersurfaces. (AM-61), Volume 61, will be forthcoming.

    • Mathematics

Singularities and Foliations. Geometry, Topology and Applications

BMMS 2/NBMS 3, Salvador, Brazil, 2015
Author: Raimundo Nonato Araújo dos Santos,Aurélio Menegon Neto,David Mond,Marcelo J. Saia,Jawad Snoussi
Publisher: Springer
ISBN: 3319736396
Category: Mathematics
Page: 553
View: 6709
This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully peer-reviewed and revised, and cover topics like Equisingularity, Topology and Geometry of Singularities, Topological Classification of Singularities of Mappings, and more. They were written by mathematicians from several countries, including Brazil, Spain, Mexico, Japan and the USA, on relevant topics on Theory of Singularity, such as studies on deformations, Milnor fibration, foliations, Catastrophe theory, and myriad applications. Open problems are also introduced, making this volume a must-read both for graduate students and active researchers in this field.

    • Mathematics

Introduction to Singularities


Author: Shihoko Ishii
Publisher: Springer
ISBN: 443155081X
Category: Mathematics
Page: 223
View: 7419
This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundaries of which correspond to singular varieties. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dim ensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied.

Deformations of singularities


Author: Jan Stevens
Publisher: Springer Science & Business Media
ISBN: 9783540005605
Category:
Page: 115
View: 5159

    • Mathematics

Isolated Singular Points on Complete Intersections


Author: Eduard Looijenga
Publisher: Cambridge University Press
ISBN: 0521286743
Category: Mathematics
Page: 200
View: 1994
This book will be of use to professional mathematicians working in algebraic geometry, complex-analytical geometry and, to some extent, differential analysis.

    • Mathematics

Milnor Fiber Boundary of a Non-isolated Surface Singularity


Author: András Némethi,Ágnes Szilárd
Publisher: Springer Science & Business Media
ISBN: 3642236464
Category: Mathematics
Page: 240
View: 6354
In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging non-isolated case. Let f be a complex analytic hypersurface germ in three variables whose zero set has a 1-dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber of f as an oriented plumbed 3-manifold. This method also provides the characteristic polynomial of the algebraic monodromy. We then determine the multiplicity system of the open book decomposition of M cut out by the argument of g for any complex analytic germ g such that the pair (f,g) is an ICIS. Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (f,g) are also described. The theory is supported by a substantial amount of examples, including homogeneous and composed singularities and suspensions. The properties peculiar to M are also emphasized.

    • Mathematics

New Developments in Singularity Theory


Author: Dirk Siersma,Charles Wall,V. Zakalyukin
Publisher: Springer Science & Business Media
ISBN: 9401008345
Category: Mathematics
Page: 472
View: 4973
Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions. The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters. The articles collected here can be grouped under three headings. (A) Singularities of real maps; (B) Singular complex variables; and (C) Singularities of homomorphic maps.

    • Mathematics

Theory of Singularities and Its Applications


Author: Vladimir Igorevich Arnolʹd
Publisher: American Mathematical Soc.
ISBN: 9780821841006
Category: Mathematics
Page: 333
View: 5880
The theory of singularities lies at the crossroads between those branches of mathematics which are the most abstract and those which are the most applied. Algebraic and differential geometry and topology, commutative algebra and group theory are as intimately connected to singularity theory as are dynamical systems theory, control theory, differential equations, quantum mechanical and quasi-classical asymptotics, optics, and functional analysis. This collection of papers incorporates recent results of participants in the editor's ongoing seminar in singularity theory, held in the Mechanics and Mathematics Department of Moscow University for over twenty years. With its broad range of subject matter, this volume will appeal to a wide range of readers in various areas of the mathematical sciences.Among the topics covered are: construction of new knot invariants, stable cohomology of complementary spaces to diffusion diagrams, topological properties of spaces of Legendre maps, application of Weierstrass bifurcation points in projective curve flattenings, classification of singularities of projective surfaces with boundary, nonsmoothness of visible contours of smooth convex hypersurfaces, flag manifolds, hyperbolic partial differential systems, and control theory.

    • Mathematics

Singularities

Proceedings of the IMA Participating Institutions Conference Held July 28-August 1, 1986, with Support from the Participating Institutions of the Institute for Mathematics and Its Applications and the University of Iowa
Author: Richard Randell,Institute for Mathematics and Its Applications
Publisher: American Mathematical Soc.
ISBN: 0821850962
Category: Mathematics
Page: 359
View: 9248
This volume contains the proceedings of the Institute for Mathematics and its Applications Participating Institutions Conference on Singularities, held at the University of Iowa in July 1986. The conference brought together an international group of researchers in algebraic and analytic singularity theory. This collection consists of research papers related to talks given at the conference. The field of singularities takes techniques from and gives results to many areas of mathematics, including algebraic and differential geometry and topology, complex analysis, Lie algebras and reflection groups, and combinatorics. All these areas are represented here with an emphasis on local algebraic, analytic and tangential properties, deformation and topology of singularities, and arrangements of hyperplanes.This volume will be of interest to current and prospective researchers in various aspects of singularity theory, as it provides an overview of the current state of singularity theory and details work in several subareas. Many of the articles provide a basis for further research, and a list of problems presented at the conference is included.

    • Mathematics

Sheaves in Topology


Author: Alexandru Dimca
Publisher: Springer Science & Business Media
ISBN: 3642188680
Category: Mathematics
Page: 240
View: 3222
Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds. This introduction to the subject can be regarded as a textbook on modern algebraic topology, treating the cohomology of spaces with sheaf (as opposed to constant) coefficients. The author helps readers progress quickly from the basic theory to current research questions, thoroughly supported along the way by examples and exercises.

    • Mathematics

Mathematical Reviews


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 9848

    • Mathematics

Handbook of Teichmüller Theory


Author: Athanase Papadopoulos
Publisher: European Mathematical Society
ISBN: 9783037191033
Category: Mathematics
Page: 866
View: 1167

    • Mathematics

The Cauchy Method of Residues

Theory and Applications
Author: Dragonslav Mitrinovic,J.D. Keckic
Publisher: Springer Science & Business Media
ISBN: 9789027716231
Category: Mathematics
Page: 361
View: 6620
Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not' grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory arid the struc ture of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-5cale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics. This program, Mathematics and Its Applications, is devoted to such (new) interrelations as exampla gratia: - a central concept which plays an important role in several different mathe matical and/or scientific specialized areas; - new applications of the results and ideas from one area of scientific en deavor into another; - influences which the results, problems and concepts of one field of enquiry have and have had on the development of another.

    • Mathematics

Numerical Control over Complex Analytic Singularities


Author: David B. Massey
Publisher: American Mathematical Soc.
ISBN: 0821832808
Category: Mathematics
Page: 268
View: 3418
The Milnor number is a powerful invariant of an isolated, complex, affine hyper surface singularity. It provides data about the local, ambient, topological-type of the hyper surface, and the constancy of the Milnor number throughout a family implies that Thom's $a_f$ condition holds and that the local, ambient, topological-type is constant in the family. Much of the usefulness of the Milnor number is due to the fact that it can be effectively calculated in an algebraic manner.The Le cycles and numbers are a generalization of the Milnor number to the setting of complex, affine hyper surface singularities, where the singular set is allowed to be of arbitrary dimension. As with the Milnor number, the Le numbers provide data about the local, ambient, topological-type of the hyper surface, and the constancy of the Le numbers throughout a family implies that Thom's $a_f$ condition holds and that the Milnor fibrations are constant throughout the family. Again, much of the usefulness of the Le numbers is due to the fact that they can be effectively calculated in an algebraic manner.In this work, we generalize the Le cycles and numbers to the case of hyper surfaces inside arbitrary analytic spaces. We define the Le-Vogel cycles and numbers, and prove that the Le-Vogel numbers control Thom's $a_f$ condition. We also prove a relationship between the Euler characteristic of the Milnor fibre and the Le-Vogel numbers. Moreover, we give examples which show that the Le-Vogel numbers are effectively calculable. In order to define the Le-Vogel cycles and numbers, we require, and include, a great deal of background material on Vogel cycles, analytic intersection theory, and the derived category. Also, to serve as a model case for the Le-Vogel cycles, we recall our earlier work on the Le cycles of an affine hyper surface singularity.

    • Mathematics

Singularities


Author: Jean-Paul Brasselet,Unité de recherche associée au CNRS' Geometry, Analysis, and Topology
Publisher: Cambridge University Press
ISBN: 9780521466318
Category: Mathematics
Page: 419
View: 9178
This book contains papers given at the International Singularity Conference held in 1991 at Lille.

    • Mathematics

Singularities


Author: Peter Orlik,American Mathematical Society
Publisher: American Mathematical Soc.
ISBN: 0821814664
Category: Mathematics
Page: 680
View: 5640
On April 7-10, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincari, held at Indiana University, Bloomington, Indiana. This work presents the written versions of all but three of the invited talks presented at this Symposium. It contains 2 papers by invited speakers who aren't able to attend.

    • Mathematics

Real And Complex Singularities


Author: David Mond,Marcelo Saia
Publisher: CRC Press
ISBN: 9780203912089
Category: Mathematics
Page: 336
View: 8820
This text offers a selection of papers on singularity theory presented at the Sixth Workshop on Real and Complex Singularities held at ICMC-USP, Brazil. It should help students and specialists to understand results that illustrate the connections between singularity theory and related fields. The authors discuss irreducible plane curve singularities, openness and multitransversality, the distribution Afs and the real asymptotic spectrum, deformations of boundary singularities and non-crystallographic coxeter groups, transversal Whitney topology and singularities of Haefliger foliations, the topology of hypersurface singularities, polar multiplicities and equisingularity of map germs from C3 to C4, and topological invariants of stable maps from a surface to the plane from a global viewpoint.