Resolution Of Singularities Of Embedded Algebraic Surfaces
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Resolution Of Singularities Of Embedded Algebraic Surfaces
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Author : Shreeram S. Abhyankar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Resolution Of Singularities Of Embedded Algebraic Surfaces written by Shreeram S. Abhyankar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The common solutions of a finite number of polynomial equations in a finite number of variables constitute an algebraic variety. The degrees of freedom of a moving point on the variety is the dimension of the variety. A one-dimensional variety is a curve and a two-dimensional variety is a surface. A three-dimensional variety may be called asolid. Most points of a variety are simple points. Singularities are special points, or points of multiplicity greater than one. Points of multiplicity two are double points, points of multiplicity three are tripie points, and so on. A nodal point of a curve is a double point where the curve crosses itself, such as the alpha curve. A cusp is a double point where the curve has a beak. The vertex of a cone provides an example of a surface singularity. A reversible change of variables gives abirational transformation of a variety. Singularities of a variety may be resolved by birational transformations.
Resolution Of Singularities Of Embedded Algebraic Surfaces
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Author : Shreeram Shankar Abhyankar
language : en
Publisher:
Release Date : 1966
Resolution Of Singularities Of Embedded Algebraic Surfaces written by Shreeram Shankar Abhyankar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Mathematics categories.
This new edition describes the geometric part of the author's 1965 proof of desingularization of algebraic surfaces and solids in nonzero characteristic. The book also provides a self-contained introduction to birational algebraic geometry, based only on basic commutative algebra. In addition, it gives a short proof of analytic desingularization in characteristic zero for any dimension found in 1996 and based on a new avatar of an algorithmic trick employed in the original edition of the book. This new edition will inspire further progress in resolution of singularities of algebraic and arithmetical varieties which will be valuable for applications to algebraic geometry and number theory. The book can be used for a second year graduate course. The reference list has been updated.
Resolution Of Singularities Of Embedded Algebraic Surfaces
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Author : Carroll Newton Smith
language : en
Publisher:
Release Date : 1966
Resolution Of Singularities Of Embedded Algebraic Surfaces written by Carroll Newton Smith and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with categories.
Resolutions Of Singularities Of Embedded Algebraic Surfaces
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Author : Shreeram Shankar Abhyankar
language : en
Publisher:
Release Date : 1966
Resolutions Of Singularities Of Embedded Algebraic Surfaces written by Shreeram Shankar Abhyankar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with categories.
Singularities In Algebraic And Analytic Geometry
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Author : Caroline Grant Melles
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Singularities In Algebraic And Analytic Geometry written by Caroline Grant Melles 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 2000 with Mathematics categories.
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.
Commutative Algebra Singularities And Computer Algebra
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Author : Jürgen Herzog
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Commutative Algebra Singularities And Computer Algebra written by Jürgen Herzog and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Proceedings of the NATO Advanced Research Workshop, held in Sinaia, Romania, 17-22 September 2002
Algebraic Geometry And Singularities
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Author : Antonio Campillo Lopez
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Algebraic Geometry And Singularities written by Antonio Campillo Lopez and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The focus of this volume lies on singularity theory in algebraic geometry. It includes papers documenting recent and original developments and methods in subjects such as resolution of singularities, D-module theory, singularities of maps and geometry of curves. The papers originate from the Third International Conference on Algebraic Geometry held in La Rbida, Spain, in December 1991. Since then, the articles have undergone a meticulous process of refereeing and improvement, and they have been organized into a comprehensive account of the state of the art in this field.
Monomialization Of Morphisms From 3 Folds To Surfaces
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Author : Steven D. Cutkosky
language : en
Publisher: Springer
Release Date : 2004-10-13
Monomialization Of Morphisms From 3 Folds To Surfaces written by Steven D. Cutkosky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-13 with Mathematics categories.
A morphism of algebraic varieties (over a field characteristic 0) is monomial if it can locally be represented in e'tale neighborhoods by a pure monomial mappings. The book gives proof that a dominant morphism from a nonsingular 3-fold X to a surface S can be monomialized by performing sequences of blowups of nonsingular subvarieties of X and S. The construction is very explicit and uses techniques from resolution of singularities. A research monograph in algebraic geometry, it addresses researchers and graduate students.
The Resolution Of Singular Algebraic Varieties
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Author : David Ellwood
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-12
The Resolution Of Singular Algebraic Varieties written by David Ellwood 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 2014-12-12 with Mathematics categories.
Resolution of Singularities has long been considered as being a difficult to access area of mathematics. The more systematic and simpler proofs that have appeared in the last few years in zero characteristic now give us a much better understanding of singularities. They reveal the aesthetics of both the logical structure of the proof and the various methods used in it. The present volume is intended for readers who are not yet experts but always wondered about the intricacies of resolution. As such, it provides a gentle and quite comprehensive introduction to this amazing field. The book may tempt the reader to enter more deeply into a topic where many mysteries--especially the positive characteristic case--await to be disclosed. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Handbook Of Geometry And Topology Of Singularities I
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Author : José Luis Cisneros Molina
language : en
Publisher: Springer Nature
Release Date : 2020-10-24
Handbook Of Geometry And Topology Of Singularities I written by José Luis Cisneros Molina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-24 with Mathematics categories.
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.