Singular Points Of Complex Hypersurfaces Am 61 Volume 61
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Singularities And Their Interaction With Geometry And Low Dimensional Topology
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Author : Javier Fernández de Bobadilla
language : en
Publisher: Springer Nature
Release Date : 2021-05-27
Singularities And Their Interaction With Geometry And Low Dimensional Topology written by Javier Fernández de Bobadilla and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-27 with Mathematics categories.
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.
Singular Algebraic Curves
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Author : Gert-Martin Greuel
language : en
Publisher: Springer
Release Date : 2018-12-30
Singular Algebraic Curves written by Gert-Martin Greuel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-30 with Mathematics categories.
Singular algebraic curves have been in the focus of study in algebraic geometry from the very beginning, and till now remain a subject of an active research related to many modern developments in algebraic geometry, symplectic geometry, and tropical geometry. The monograph suggests a unified approach to the geometry of singular algebraic curves on algebraic surfaces and their families, which applies to arbitrary singularities, allows one to treat all main questions concerning the geometry of equisingular families of curves, and, finally, leads to results which can be viewed as the best possible in a reasonable sense. Various methods of the cohomology vanishing theory as well as the patchworking construction with its modifications will be of a special interest for experts in algebraic geometry and singularity theory. The introductory chapters on zero-dimensional schemes and global deformation theory can well serve as a material for special courses and seminars for graduate and post-graduate students.Geometry in general plays a leading role in modern mathematics, and algebraic geometry is the most advanced area of research in geometry. In turn, algebraic curves for more than one century have been the central subject of algebraic geometry both in fundamental theoretic questions and in applications to other fields of mathematics and mathematical physics. Particularly, the local and global study of singular algebraic curves involves a variety of methods and deep ideas from geometry, analysis, algebra, combinatorics and suggests a number of hard classical and newly appeared problems which inspire further development in this research area.
Moduli Spaces Virtual Invariants And Shifted Symplectic Structures
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Author : Young-Hoon Kiem
language : en
Publisher: Springer Nature
Release Date : 2025-03-25
Moduli Spaces Virtual Invariants And Shifted Symplectic Structures written by Young-Hoon Kiem and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-25 with Mathematics categories.
Enumerative geometry is a core area of algebraic geometry that dates back to Apollonius in the second century BCE. It asks for the number of geometric figures with desired properties and has many applications from classical geometry to modern physics. Typically, an enumerative geometry problem is solved by first constructing the space of all geometric figures of fixed type, called the moduli space, and then finding the subspace of objects satisfying the desired properties. Unfortunately, many moduli spaces from nature are highly singular, and an intersection theory is difficult to make sense of. However, they come with deeper structures, such as perfect obstruction theories, which enable us to define nice subsets, called virtual fundamental classes. Now, enumerative numbers, called virtual invariants, are defined as integrals against the virtual fundamental classes. Derived algebraic geometry is a relatively new area of algebraic geometry that is a natural generalization of Serre’s intersection theory in the 1950s and Grothendieck’s scheme theory in the 1960s. Many moduli spaces in enumerative geometry admit natural derived structures as well as shifted symplectic structures. The book covers foundations on derived algebraic and symplectic geometry. Then, it covers foundations on virtual fundamental classes and moduli spaces from a classical algebraic geometry point of view. Finally, it fuses derived algebraic geometry with enumerative geometry and covers the cutting-edge research topics about Donaldson–Thomas invariants in dimensions three and four.
Singularities And Computer Algebra
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Author : Wolfram Decker
language : en
Publisher: Springer
Release Date : 2017-03-29
Singularities And Computer Algebra written by Wolfram Decker and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-29 with Mathematics categories.
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.
Non K Hler Complex Surfaces And Strongly Pseudoconcave Surfaces
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Author : Naohiko Kasuya
language : en
Publisher: Springer Nature
Release Date : 2025-03-14
Non K Hler Complex Surfaces And Strongly Pseudoconcave Surfaces written by Naohiko Kasuya and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-14 with Mathematics categories.
The main themes of this book are non-Kähler complex surfaces and strongly pseudoconcave complex surfaces. Though there are several notable examples of compact non-Kähler surfaces, including Hopf surfaces, Kodaira surfaces, and Inoue surfaces, these subjects have been regarded as secondary to Kähler manifolds and strongly pseudoconvex manifolds. Recently, however, the existence of uncountably many non-Kähler complex structures on the 4-dimensional Euclidean space has been shown by Di Scala, Kasuya, and Zuddas through their construction. Furthermore, Kasuya and Zuddas' handlebody construction reveals that strongly pseudoconcave surfaces have flexibility with respect to both four-dimensional topology and boundary contact structures. These constructions are based on the knowledge of differential topology and contact geometry, and provide examples of fruitful applications of these areas to complex geometry. Thus, for (especially non-compact) non-Kähler complex surfaces and strongly pseudoconcave complex surfaces, it is not an exaggeration to say that the research is still in its infancy, with numerous areas yet to be explored and expected to develop in the future.
Introduction To Singularities
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Author : Shihoko Ishii
language : en
Publisher: Springer
Release Date : 2018-09-21
Introduction To Singularities written by Shihoko Ishii and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-21 with Mathematics categories.
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 bookis 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.
Singularities Of Plane Curves
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Author : Eduardo Casas-Alvero
language : en
Publisher: Cambridge University Press
Release Date : 2000-08-31
Singularities Of Plane Curves written by Eduardo Casas-Alvero 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 2000-08-31 with Mathematics categories.
Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.
The Geometry And Topology Of Coxeter Groups
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Author : Michael W. Davis
language : en
Publisher: Springer Nature
Release Date : 2025-07-30
The Geometry And Topology Of Coxeter Groups written by Michael W. Davis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-30 with Mathematics categories.
This book, now in a revised and extended second edition, offers an in-depth account of Coxeter groups through the perspective of geometric group theory. It examines the connections between Coxeter groups and major open problems in topology related to aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer Conjectures. The book also discusses key topics in geometric group theory and topology, including Hopf’s theory of ends, contractible manifolds and homology spheres, the Poincaré Conjecture, and Gromov’s theory of CAT(0) spaces and groups. In addition, this second edition includes new chapters on Artin groups and their Betti numbers. Written by a leading expert, the book is an authoritative reference on the subject.
Concerning The Hilbert 16th Problem
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Author : S. Yakovenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Concerning The Hilbert 16th Problem written by S. Yakovenko 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 1995 with Differential equations categories.
Singularities And Foliations Geometry Topology And Applications
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Author : Raimundo Nonato Araújo dos Santos
language : en
Publisher: Springer
Release Date : 2018-03-21
Singularities And Foliations Geometry Topology And Applications written by Raimundo Nonato Araújo dos Santos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-21 with Mathematics categories.
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.