Singularities Ii

Author : Jean-Paul Brasselet
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 52,7 Mb
Release : 2008
Category : Singularities (Mathematics)
ISBN : 9780821847176

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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 : José Luis Cisneros-Molina,Dũng Tráng Lê,José Seade
Publisher : Springer Nature
Page : 581 pages
File Size : 48,7 Mb
Release : 2021-11-01
Category : Mathematics
ISBN : 9783030780241

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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 : Martin Golubitsky,David G. Schaeffer
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 42,5 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461250340

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Singularities and Groups in Bifurcation Theory by Martin Golubitsky,David G. Schaeffer Pdf

This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob lems and we hope to convert the reader to this view. In this preface we will discuss what we feel are the strengths of the singularity theory approach. This discussion then Ieads naturally into a discussion of the contents of the book and the prerequisites for reading it. Let us emphasize that our principal contribution in this area has been to apply pre-existing techniques from singularity theory, especially unfolding theory and classification theory, to bifurcation problems. Many ofthe ideas in this part of singularity theory were originally proposed by Rene Thom; the subject was then developed rigorously by John Matherand extended by V. I. Arnold. In applying this material to bifurcation problems, we were greatly encouraged by how weil the mathematical ideas of singularity theory meshed with the questions addressed by bifurcation theory. Concerning our title, Singularities and Groups in Bifurcation Theory, it should be mentioned that the present text is the first volume in a two-volume sequence. In this volume our emphasis is on singularity theory, with group theory playing a subordinate role. In Volume II the emphasis will be more balanced. Having made these remarks, Iet us set the context for the discussion of the strengths of the singularity theory approach to bifurcation. As we use the term, bifurcation theory is the study of equations with multiple solutions.

Author : Caroline Grant Melles,Ruth Ingrid Michler
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 55,7 Mb
Release : 2000
Category : Singularities (Mathematics)
ISBN : 9780821820056

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Singularities in Algebraic and Analytic Geometry by Caroline Grant Melles,Ruth Ingrid Michler Pdf

This volume contains the proceedings of an AMS special session held at the 1999 Joint Mathematics Meetings in San Antonio. The participants were an international group of researchers studying singularities from algebraic and analytic viewpoints. The contributed papers contain original results as well as some expository and historical material. This volume is dedicated to Oscar Zariski, on the one hundredth anniversary of his birth. Topics include the role of valuation theory in algebraic geometry with recent applications to the structure of morphisms; algorithmic approaches to resolution of equisingular surface singularities and locally toric varieties; weak subintegral closures of ideals and Rees valuations; constructions of universal weakly subintegral extensions of rings; direct-sum decompositions of finitely generated modules; construction and examples of resolution graphs of surface singularities; Jacobians of meromorphic curves; investigation of spectral numbers of curve singularities using Puiseux pairs; Gröbner basis calculations of Hochschild homology for hypersurfaces with isolated singularities; and the theory of characteristic classes of singular spaces - a brief history with conjectures and open problems.

Author : Victor Goryunov,Kevin Houston,Roberta Wik-Atique
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 49,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821853597

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Real and Complex Singularities by Victor Goryunov,Kevin Houston,Roberta Wik-Atique Pdf

"This volume is a collection of papers presented at the 11th International Workshop on Real and Complex Singularities, held July 26-30, 2010, in Säao Carlos, Brazil, in honor of David Mond's 60th birthday. This volume reflects the high level of the conference discussing the most recent results and applications of singularity theory. Articles in the first part cover pure singularity theory: invariants, classification theory, and Milnor fibres. Articles in the second part cover singularities in topology and differential geometry, as well as algebraic geometry and bifurcation theory: Artin-Greenberg function of a plane curve singularity, metric theory of singularities, symplectic singularities, cobordisms of fold maps, Goursat distributions, sections of analytic varieties, Vassiliev invariants, projections of hypersurfaces, and linearity of the Jacobian ideal."--P. [4] of cover.

Author : José Seade
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 44,7 Mb
Release : 2006-03-21
Category : Mathematics
ISBN : 9783764373955

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On the Topology of Isolated Singularities in Analytic Spaces by José Seade Pdf

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.

Author : János Kollár
Publisher : Cambridge University Press
Page : 381 pages
File Size : 47,9 Mb
Release : 2013-02-21
Category : Mathematics
ISBN : 9781107311473

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Singularities of the Minimal Model Program by János Kollár Pdf

This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities and the development of Mori's program have been deeply intertwined. Early work on minimal models relied on detailed study of terminal and canonical singularities but many later results on log terminal singularities were obtained as consequences of the minimal model program. Recent work on the abundance conjecture and on moduli of varieties of general type relies on subtle properties of log canonical singularities and conversely, the sharpest theorems about these singularities use newly developed special cases of the abundance problem. This book untangles these interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results.

Author : Terence Gaffney,Maria Aparecida Soares Ruas
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 43,6 Mb
Release : 2004
Category : Singularities (Mathematics)
ISBN : 9780821836651

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Real and Complex Singularities by Terence Gaffney,Maria Aparecida Soares Ruas Pdf

The Workshop on Real and Complex Singularities is held every other year at the Instituto de Ciencias Matematicas e de Computacao (Sao Carlos, Brazil) and brings together specialists in the vanguard of singularities and its applications. This volume contains articles contributed by participants of the seventh workshop. The included papers reflect Fields Medalist Rene Thom's original vision of singularities and represent all branches of the subject: equisingularity of sets and mappings, the geometry of singular complex analytic sets, singularities of mappings and their elimination, characteristic classes, applications to differential geometry, differential equations, and bifurcation theory. The book is suitable for graduate students and researchers interested in singularity theory.

Author : José Luis Cisneros-Molina,Lê Dũng Tráng,José Seade
Publisher : Springer Nature
Page : 622 pages
File Size : 54,6 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 : Mariano Giaquinta,Guiseppe Modica,Jiri Soucek
Publisher : Springer Science & Business Media
Page : 728 pages
File Size : 48,7 Mb
Release : 1998-08-19
Category : Mathematics
ISBN : 354064010X

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Cartesian Currents in the Calculus of Variations II by Mariano Giaquinta,Guiseppe Modica,Jiri Soucek Pdf

This monograph (in two volumes) deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configuations in nonlinear elasticity or for liquid crystals. The presentation is selfcontained and accessible to non specialists. Topics are treated as far as possible in an elementary way, illustrating results with simple examples; in principle, chapters and even sections are readable independently of the general context, so that parts can be easily used for graduate courses. Open questions are often mentioned and the final section of each chapter discusses references to the literature and sometimes supplementary results. Finally, a detailed Table of Contents and an extensive Index are of help to consult this monograph

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 41,5 Mb
Release : 2024-06-10
Category : Electronic
ISBN : 9789814477048

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Singularities in Geometry and Topology by Anonim Pdf

Author : Gert-Martin Greuel,Luis Narváez Macarro,Sebastià Xambó-Descamps
Publisher : Springer
Page : 604 pages
File Size : 43,9 Mb
Release : 2018-09-18
Category : Mathematics
ISBN : 9783319968278

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Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics by Gert-Martin Greuel,Luis Narváez Macarro,Sebastià Xambó-Descamps Pdf

This volume brings together recent, original research and survey articles by leading experts in several fields that include singularity theory, algebraic geometry and commutative algebra. The motivation for this collection comes from the wide-ranging research of the distinguished mathematician, Antonio Campillo, in these and related fields. Besides his influence in the mathematical community stemming from his research, Campillo has also endeavored to promote mathematics and mathematicians' networking everywhere, especially in Spain, Latin America and Europe. Because of his impressive achievements throughout his career, we dedicate this book to Campillo in honor of his 65th birthday. Researchers and students from the world-wide, and in particular Latin American and European, communities in singularities, algebraic geometry, commutative algebra, coding theory, and other fields covered in the volume, will have interest in this book.

Author : Javier Fernández de Bobadilla,Tamás László,András Stipsicz
Publisher : Springer Nature
Page : 332 pages
File Size : 50,9 Mb
Release : 2021-05-27
Category : Mathematics
ISBN : 9783030619589

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Singularities and Their Interaction with Geometry and Low Dimensional Topology by Javier Fernández de Bobadilla,Tamás László,András Stipsicz Pdf

The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory. The papers, written by leading researchers working on various topics of the above fields, are the outcome of the “Némethi60: Geometry and Topology of Singularities” conference held at the Alfréd Rényi Institute of Mathematics in Budapest, from May 27 to 31, 2019. Both the conference and this resulting volume are in honor of Professor András Némethi, on the occasion of his 60th birthday, whose work plays a decisive and influential role in the interactions between the above fields. The book should serve as a valuable resource for graduate students and researchers to deepen the new perspectives, methods, and connections between geometry and topology regarding singularities.

Author : Claus Hertling
Publisher : Cambridge University Press
Page : 292 pages
File Size : 50,9 Mb
Release : 2002-07-25
Category : Mathematics
ISBN : 0521812968

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Frobenius Manifolds and Moduli Spaces for Singularities by Claus Hertling Pdf

This book presents the theory of Frobenius manifolds, as well as all the necessary tools and several applications.

Author : Shihoko Ishii
Publisher : Springer
Page : 236 pages
File Size : 52,7 Mb
Release : 2018-09-21
Category : Mathematics
ISBN : 9784431568377

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Introduction to Singularities by Shihoko Ishii Pdf

This book is an introduction to singularities for graduate students and researchers. Algebraic geometry is said to have 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. First, mostly non-singular varieties were studied. 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. 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-dimensional 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. In the second edition, brief descriptions about recent remarkable developments of the researches are added as the last chapter.