Trends In Singularities

Author : Anatoly Libgober,Mihai Tibar
Publisher : Birkhäuser
Page : 250 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034881616

Get Book

Trends in Singularities by Anatoly Libgober,Mihai Tibar Pdf

The collection of papers in this volume represents recent advances in the under standing of the geometry and topology of singularities. The book covers a broad range of topics which are in the focus of contemporary singularity theory. Its idea emerged during two Singularities workshops held at the University of Lille (USTL) in 1999 and 2000. Due to the breadth of singularity theory, a single volume can hardly give the complete picture of today's progress. Nevertheless, this collection of papers provides a good snapshot of what is the state of affairs in the field, at the turn of the century. Several papers deal with global aspects of singularity theory. Classification of fam ilies of plane curves with prescribed singularities were among the first problems in algebraic geometry. Classification of plane cubics was known to Newton and classification of quartics was achieved by Klein at the end of the 19th century. The problem of classification of curves of higher degrees was addressed in numerous works after that. In the paper by Artal, Carmona and Cogolludo, the authors de scribe irreducible sextic curves having a singular point of type An (n > 15) and a large (Le. , :::: 18) sum of Milnor numbers of other singularities. They have discov ered many interesting properties of these families. In particular they have found new examples of so-called Zariski pairs, i. e.

Author : Anatoly Libgober,Mihai Tibar
Publisher : Birkhäuser
Page : 246 pages
File Size : 45,7 Mb
Release : 2012-10-29
Category : Mathematics
ISBN : 3034894619

Get Book

Trends in Singularities by Anatoly Libgober,Mihai Tibar Pdf

The collection of papers in this volume represents recent advances in the under standing of the geometry and topology of singularities. The book covers a broad range of topics which are in the focus of contemporary singularity theory. Its idea emerged during two Singularities workshops held at the University of Lille (USTL) in 1999 and 2000. Due to the breadth of singularity theory, a single volume can hardly give the complete picture of today's progress. Nevertheless, this collection of papers provides a good snapshot of what is the state of affairs in the field, at the turn of the century. Several papers deal with global aspects of singularity theory. Classification of fam ilies of plane curves with prescribed singularities were among the first problems in algebraic geometry. Classification of plane cubics was known to Newton and classification of quartics was achieved by Klein at the end of the 19th century. The problem of classification of curves of higher degrees was addressed in numerous works after that. In the paper by Artal, Carmona and Cogolludo, the authors de scribe irreducible sextic curves having a singular point of type An (n > 15) and a large (Le. , :::: 18) sum of Milnor numbers of other singularities. They have discov ered many interesting properties of these families. In particular they have found new examples of so-called Zariski pairs, i. e.

Author : Jean-Paul Brasselet
Publisher : World Scientific
Page : 917 pages
File Size : 52,7 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812700223

Get Book

Singularities in Geometry and Topology by Jean-Paul Brasselet Pdf

Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology.The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 47,8 Mb
Release : 2024-05-19
Category : Electronic
ISBN : 9789814477048

Get Book

Singularities in Geometry and Topology by Anonim Pdf

Author : Anatoly Libgober,Mihai Tibar
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 41,7 Mb
Release : 2002-03-01
Category : Mathematics
ISBN : 3764367040

Get Book

Trends in Singularities by Anatoly Libgober,Mihai Tibar Pdf

The collection of papers in this volume represents recent advances in the under standing of the geometry and topology of singularities. The book covers a broad range of topics which are in the focus of contemporary singularity theory. Its idea emerged during two Singularities workshops held at the University of Lille (USTL) in 1999 and 2000. Due to the breadth of singularity theory, a single volume can hardly give the complete picture of today's progress. Nevertheless, this collection of papers provides a good snapshot of what is the state of affairs in the field, at the turn of the century. Several papers deal with global aspects of singularity theory. Classification of fam ilies of plane curves with prescribed singularities were among the first problems in algebraic geometry. Classification of plane cubics was known to Newton and classification of quartics was achieved by Klein at the end of the 19th century. The problem of classification of curves of higher degrees was addressed in numerous works after that. In the paper by Artal, Carmona and Cogolludo, the authors de scribe irreducible sextic curves having a singular point of type An (n > 15) and a large (Le. , :::: 18) sum of Milnor numbers of other singularities. They have discov ered many interesting properties of these families. In particular they have found new examples of so-called Zariski pairs, i. e.

Author : András Némethi
Publisher : Springer Nature
Page : 732 pages
File Size : 40,5 Mb
Release : 2022-10-07
Category : Mathematics
ISBN : 9783031067532

Get Book

Normal Surface Singularities by András Némethi Pdf

This monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology. In this way, it unites the analytic approach with the more recent topological one, combining their tools and methods. In the first chapters, the book sets out the foundations of the theory of normal surface singularities. This includes a comprehensive presentation of the properties of the link (as an oriented 3-manifold) and of the invariants associated with a resolution, combined with the structure and special properties of the line bundles defined on a resolution. A recurring theme is the comparison of analytic and topological invariants. For example, the Poincaré series of the divisorial filtration is compared to a topological zeta function associated with the resolution graph, and the sheaf cohomologies of the line bundles are compared to the Seiberg–Witten invariants of the link. Equivariant Ehrhart theory is introduced to establish surgery-additivity formulae of these invariants, as well as for the regularization procedures of multivariable series. In addition to recent research, the book also provides expositions of more classical subjects such as the classification of plane and cuspidal curves, Milnor fibrations and smoothing invariants, the local divisor class group, and the Hilbert–Samuel function. It contains a large number of examples of key families of germs: rational, elliptic, weighted homogeneous, superisolated and splice-quotient. It provides concrete computations of the topological invariants of their links (Casson(–Walker) and Seiberg–Witten invariants, Turaev torsion) and of the analytic invariants (geometric genus, Hilbert function of the divisorial filtration, and the analytic semigroup associated with the resolution). The book culminates in a discussion of the topological and analytic lattice cohomologies (as categorifications of the Seiberg–Witten invariant and of the geometric genus respectively) and of the graded roots. Several open problems and conjectures are also formulated. Normal Surface Singularities provides researchers in algebraic and differential geometry, singularity theory, complex analysis, and low-dimensional topology with an invaluable reference on this rich topic, offering a unified presentation of the major results and approaches.

Author : Jean-Paul Brasselet
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 50,8 Mb
Release : 2008
Category : Singularities (Mathematics)
ISBN : 9780821847176

Get Book

Singularities II by Jean-Paul Brasselet Pdf

"This is the second part of the Proceedings of the meeting "School and Workshop on the Geometry and Topology of Singularities", held in Cuemavaca, Mexico, from January 8th to 26th of 2007, in celebration of the 60th Birthday of Le Dung Trang." "This volume contains fourteen cutting-edge research articles on geometric and topological aspects of singularities of spaces and maps. By reading this volume, and the accompanying volume on algebraic and analytic aspects of singularities, the reader should gain an appreciation for the depth, breadth, and beauty of the subject, and also find a rich source of questions and problems for future study."--BOOK JACKET.

Author : M. Manoel,M. C. Romero Fuster,C. T. C. Wall
Publisher : Cambridge University Press
Page : 413 pages
File Size : 40,9 Mb
Release : 2010-10-07
Category : Mathematics
ISBN : 9781139489911

Get Book

Real and Complex Singularities by M. Manoel,M. C. Romero Fuster,C. T. C. Wall Pdf

The biennial meetings at São Carlos have helped create a worldwide community of experts and young researchers working on singularity theory, with a special focus on applications to topics in both pure and applied mathematics. This volume brings together surveys and recent work from the tenth São Carlos meeting.

Author : Walter Neumann,Anne Pichon
Publisher : Springer Nature
Page : 356 pages
File Size : 40,6 Mb
Release : 2021-01-11
Category : Mathematics
ISBN : 9783030618070

Get Book

Introduction to Lipschitz Geometry of Singularities by Walter Neumann,Anne Pichon Pdf

This book presents a broad overview of the important recent progress which led to the emergence of new ideas in Lipschitz geometry and singularities, and started to build bridges to several major areas of singularity theory. Providing all the necessary background in a series of introductory lectures, it also contains Pham and Teissier's previously unpublished pioneering work on the Lipschitz classification of germs of plane complex algebraic curves. While a real or complex algebraic variety is topologically locally conical, it is in general not metrically conical; there are parts of its link with non-trivial topology which shrink faster than linearly when approaching the special point. The essence of the Lipschitz geometry of singularities is captured by the problem of building classifications of the germs up to local bi-Lipschitz homeomorphism. The Lipschitz geometry of a singular space germ is then its equivalence class in this category. The book is aimed at graduate students and researchers from other fields of geometry who are interested in studying the multiple open questions offered by this new subject.

Author : José Luis Cisneros-Molina,Dũng Tráng Lê,Mutsuo Oka,Jawad Snoussi
Publisher : Birkhäuser
Page : 231 pages
File Size : 49,7 Mb
Release : 2017-02-13
Category : Mathematics
ISBN : 9783319393391

Get Book

Singularities in Geometry, Topology, Foliations and Dynamics by José Luis Cisneros-Molina,Dũng Tráng Lê,Mutsuo Oka,Jawad Snoussi Pdf

This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings. Singularity theory is at the crossroad of various branches of mathematics and science in general. In recent years there have been remarkable developments, both in the theory itself and in its relations with other areas. The contributions in this volume originate from the “Workshop on Singularities in Geometry, Topology, Foliations and Dynamics”, held in Merida, Mexico, in December 2014, in celebration of José Seade’s 60th Birthday. It is intended for researchers and graduate students interested in singularity theory and its impact on other fields.

Author : Ana Claudia Nabarro,Juan J. Nuño-Ballesteros,Raúl Oset Sinha,Maria Aparecida Soares Ruas
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 50,7 Mb
Release : 2016-10-25
Category : Differential geometry -- Classical differential geometry -- Classical differential geometry
ISBN : 9781470422059

Get Book

Real and Complex Singularities by Ana Claudia Nabarro,Juan J. Nuño-Ballesteros,Raúl Oset Sinha,Maria Aparecida Soares Ruas Pdf

This volume is a collection of papers presented at the XIII International Workshop on Real and Complex Singularities, held from July 27–August 8, 2014, in São Carlos, Brazil, in honor of María del Carmen Romero Fuster's 60th birthday. The volume contains the notes from two mini-courses taught during the workshop: on intersection homology by J.-P. Brasselet, and on non-isolated hypersurface singularities and Lê cycles by D. Massey. The remaining contributions are research articles which cover topics from the foundations of singularity theory (including classification theory and invariants) to topology of singular spaces (links of singularities and semi-algebraic sets), as well as applications to topology (cobordism and Lefschetz fibrations), dynamical systems (Morse-Bott functions) and differential geometry (affine geometry, Gauss-maps, caustics, frontals and non-Euclidean geometries). This book is published in cooperation with Real Sociedad Matemática Española (RSME)

Author : José Luis Cisneros-Molina,Dũng Tráng Lê,José Seade
Publisher : Springer Nature
Page : 581 pages
File Size : 55,5 Mb
Release : 2021-11-01
Category : Mathematics
ISBN : 9783030780241

Get Book

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

This is the second volume of the Handbook of the Geometry and Topology of Singularities, 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. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory and related topics. 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, and 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 : Francisco-Jesús Castro-Jiménez,David Bradley Massey,Bernard Teissier,Meral Tosun
Publisher : American Mathematical Soc.
Page : 217 pages
File Size : 54,8 Mb
Release : 2020-01-13
Category : Education
ISBN : 9781470447922

Get Book

A Panorama of Singularities by Francisco-Jesús Castro-Jiménez,David Bradley Massey,Bernard Teissier,Meral Tosun Pdf

This volume contains the proceedings of the conference A Panorama on Singular Varieties, celebrating the 70th birthday of Lê Dũng Tráng, held from February 7–10, 2017, at the University of Seville, IMUS, Seville, Spain. The articles cover a wide range of topics in the study of singularities and should be of great value to graduate students and research faculty who have a basic background in the theory of singularities.

Author : Wolfram Decker,Gerhard Pfister,Mathias Schulze
Publisher : Springer
Page : 389 pages
File Size : 44,9 Mb
Release : 2017-03-29
Category : Mathematics
ISBN : 9783319288291

Get Book

Singularities and Computer Algebra by Wolfram Decker,Gerhard Pfister,Mathias Schulze Pdf

This book arose from a conference on “Singularities and Computer Algebra” which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel’s 70th birthday. This unique volume presents a collection of recent original research by some of the leading figures in singularity theory on a broad range of topics including topological and algebraic aspects, classification problems, deformation theory and resolution of singularities. At the same time, the articles highlight a variety of techniques, ranging from theoretical methods to practical tools from computer algebra.Greuel himself made major contributions to the development of both singularity theory and computer algebra. With Gerhard Pfister and Hans Schönemann, he developed the computer algebra system SINGULAR, which has since become the computational tool of choice for many singularity theorists.The book addresses researchers whose work involves singularity theory and computer algebra from the PhD to expert level.

Author : Denis Ch‚niot
Publisher : World Scientific
Page : 1083 pages
File Size : 55,7 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812704108

Get Book

Singularity Theory by Denis Ch‚niot 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.