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Complex Hypersurface Singularities With Application In Complex Geometry Algebraic Geometry And Lie Algebra
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Book Synopsis Complex Hypersurface Singularities with Application in Complex Geometry, Algebraic Geometry and Lie Algebra by : Stephen Shing-Toung Yau
Download or read book Complex Hypersurface Singularities with Application in Complex Geometry, Algebraic Geometry and Lie Algebra written by Stephen Shing-Toung Yau and published by . This book was released on 1993 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Singularities and Deformations by : Gert-Martin Greuel
Download or read book Introduction to Singularities and Deformations written by Gert-Martin Greuel and published by Springer Science & Business Media. This book was released on 2007-02-23 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Handbook of Geometry and Topology of Singularities I by : José Luis Cisneros Molina
Download or read book Handbook of Geometry and Topology of Singularities I written by José Luis Cisneros Molina and published by Springer Nature. This book was released on 2020-10-24 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Complex Geometry and Lie Theory by : James A. Carlson
Download or read book Complex Geometry and Lie Theory written by James A. Carlson and published by American Mathematical Soc.. This book was released on 1991 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the late 1960s and early 1970s, Phillip Griffiths and his collaborators undertook a study of period mappings and variation of Hodge structure. The motivating problems, which centered on the understanding of algebraic varieties and the algebraic cycles on them, came from algebraic geometry. However, the techiques used were transcendental in nature, drawing heavily on both Lie theory and hermitian differential geometry. Promising approaches were formulated to fundamental questions in the theory of algebraic curves, moduli theory, and the deep interaction between Hodge theory and algebraic cyles. Rapid progress on many fronts was made in the 1970s and 1980s, including the discovery of important connections to other fields, including Nevanlinna theory, integrable systems, rational homotopy theory, harmonic mappings, intersection cohomology, and superstring theory. This volume contains thirteen papers presented during the Symposium on Complex Geometry and Lie Theory held in Sundance, Utah in May 1989. The symposium was designed to review twenty years of interaction between these two fields, concentrating on their links with Hodge theory. The organizers felt that the time was right to examine once again the large issues of understanding the moduli and cycle theory of higher-dimensional varieties, which was the starting point of these developments. The breadth of this collection of papers indicates the continuing growth and vitality of this area of research. Several survey papers are included, which should make the book a valuable resource for graduate students and other researchers who wish to learn about the field. With contributions from some of the field's top researchers, this volume testifies to the breadth and vitality of this area of research.
Book Synopsis Principles of Algebraic Geometry by : Phillip Griffiths
Download or read book Principles of Algebraic Geometry written by Phillip Griffiths and published by John Wiley & Sons. This book was released on 2014-08-21 with total page 837 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds.
Author :Camille Laurent-Gengoux Publisher :Springer Science & Business Media ISBN 13 :3642310907 Total Pages :470 pages Book Rating :4.6/5 (423 download)
Book Synopsis Poisson Structures by : Camille Laurent-Gengoux
Download or read book Poisson Structures written by Camille Laurent-Gengoux and published by Springer Science & Business Media. This book was released on 2012-08-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.
Book Synopsis Applications of Algebraic Geometry to Coding Theory, Physics and Computation by : Ciro Ciliberto
Download or read book Applications of Algebraic Geometry to Coding Theory, Physics and Computation written by Ciro Ciliberto and published by Springer Science & Business Media. This book was released on 2001-08-31 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Research Workshop, held in Eilat, Israel, from 25th February to 1st March 2001
Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Undergraduate Algebraic Geometry by : Miles Reid
Download or read book Undergraduate Algebraic Geometry written by Miles Reid and published by Cambridge University Press. This book was released on 1988-12-15 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time. With the minimum of prerequisites, Dr Reid introduces the reader to the basic concepts of algebraic geometry including: plane conics, cubics and the group law, affine and projective varieties, and non-singularity and dimension. He is at pains to stress the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book arises from an undergraduate course given at the University of Warwick and contains numerous examples and exercises illustrating the theory.
Book Synopsis On the Topology of Isolated Singularities in Analytic Spaces by : José Seade
Download or read book On the Topology of Isolated Singularities in Analytic Spaces written by José Seade and published by Springer Science & Business Media. This book was released on 2006-03-21 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Singularities of Mappings by : David Mond
Download or read book Singularities of Mappings written by David Mond and published by Springer Nature. This book was released on 2020-01-23 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings. Part I of the book develops the now classical real C∞ and complex analytic theories jointly. Standard topics such as stability, deformation theory and finite determinacy, are covered in this part. In Part II of the book, the authors focus on the complex case. The treatment is centred around the idea of the "nearby stable object" associated to an unstable map-germ, which includes in particular the images and discriminants of stable perturbations of unstable singularities. This part includes recent research results, bringing the reader up to date on the topic. By focusing on singularities of mappings, rather than spaces, this book provides a necessary addition to the literature. Many examples and exercises, as well as appendices on background material, make it an invaluable guide for graduate students and a key reference for researchers. A number of graduate level courses on singularities of mappings could be based on the material it contains.
Book Synopsis Classical Algebraic Geometry by : Igor V. Dolgachev
Download or read book Classical Algebraic Geometry written by Igor V. Dolgachev and published by Cambridge University Press. This book was released on 2012-08-16 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.
Book Synopsis CR-Geometry and Deformations of Isolated Singularities by : Ragnar-Olaf Buchweitz
Download or read book CR-Geometry and Deformations of Isolated Singularities written by Ragnar-Olaf Buchweitz and published by American Mathematical Soc.. This book was released on 1997 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this power we show how to compute the parameter space [italic capital]X for the versal deformation of an isolated singularity ([italic capital]V, 0) under the assumptions [italic]dim [italic capital]V [greater than or equal to symbol] 4, depth {0} [italic capital]V [greater than or equal to symbol] 3, from the CR-structure on a link [italic capital]M of the singularity. We do this by showing that the space [italic capital]X is isomorphic to the space (denoted here by [script capital]K[subscript italic capital]M) associated to [italic capital]M by Kuranishi in 1977. In fact we produce isomorphisms of the associated complete local rings by producing quasi-isomorphisms of the controlling differential graded Lie algebras for the corresponding formal deformation theories.
Book Synopsis 3264 and All That by : David Eisenbud
Download or read book 3264 and All That written by David Eisenbud and published by Cambridge University Press. This book was released on 2016-04-14 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: 3264, the mathematical solution to a question concerning geometric figures.
Book Synopsis Algebraic Geometry by : Dan Abramovich
Download or read book Algebraic Geometry written by Dan Abramovich and published by American Mathematical Soc.. This book was released on 2009 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers information on various technical tools, from jet schemes and derived categories to algebraic stacks. This book delves into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties. It describes various advances in higher-dimensional bi rational geometry.
Book Synopsis Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics by : Gert-Martin Greuel
Download or read book Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics written by Gert-Martin Greuel and published by Springer. This book was released on 2018-09-18 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Singular Algebraic Curves by : Gert-Martin Greuel
Download or read book Singular Algebraic Curves written by Gert-Martin Greuel and published by Springer. This book was released on 2018-12-30 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
