Resolutions Of Singularities Of Embedded Algebraic Surfaces
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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 : 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.
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.
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.
Resolution Of Singularities
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Author : Herwig Hauser
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Resolution Of Singularities written by Herwig Hauser 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.
In September 1997, the Working Week on Resolution of Singularities was held at Obergurgl in the Tyrolean Alps. Its objective was to manifest the state of the art in the field and to formulate major questions for future research. The four courses given during this week were written up by the speakers and make up part I of this volume. They are complemented in part II by fifteen selected contributions on specific topics and resolution theories. The volume is intended to provide a broad and accessible introduction to resolution of singularities leading the reader directly to concrete research problems.
Resolution Of Singularities
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Author : Steven Dale Cutkosky
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Resolution Of Singularities written by Steven Dale Cutkosky 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 2004 with Mathematics categories.
The notion of singularity is basic to mathematics. In algebraic geometry, the resolution of singularities by simple algebraic mappings is truly a fundamental problem. It has a complete solution in characteristic zero and partial solutions in arbitrary characteristic. The resolution of singularities in characteristic zero is a key result used in many subjects besides algebraic geometry, such as differential equations, dynamical systems, number theory, the theory of $\mathcal{D}$-modules, topology, and mathematical physics. This book is a rigorous, but instructional, look at resolutions. A simplified proof, based on canonical resolutions, is given for characteristic zero. There are several proofs given for resolution of curves and surfaces in characteristic zero and arbitrary characteristic. Besides explaining the tools needed for understanding resolutions, Cutkosky explains the history and ideas, providing valuable insight and intuition for the novice (or expert). There are many examples and exercises throughout the text. The book is suitable for a second course on an exciting topic in algebraic geometry. A core course on resolutions is contained in Chapters 2 through 6. Additional topics are covered in the final chapters. The prerequisite is a course covering the basic notions of schemes and sheaves.
Resolution Of Surface Singularities
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Author : Vincent Cossart
language : en
Publisher: Springer
Release Date : 2006-11-14
Resolution Of Surface Singularities written by Vincent Cossart and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Lectures On Resolution Of Singularities Am 166
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Author : János Kollár
language : en
Publisher: Princeton University Press
Release Date : 2009-01-10
Lectures On Resolution Of Singularities Am 166 written by János Kollár and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-10 with Mathematics categories.
Resolution of singularities is a powerful and frequently used tool in algebraic geometry. In this book, János Kollár provides a comprehensive treatment of the characteristic 0 case. He describes more than a dozen proofs for curves, many based on the original papers of Newton, Riemann, and Noether. Kollár goes back to the original sources and presents them in a modern context. He addresses three methods for surfaces, and gives a self-contained and entirely elementary proof of a strong and functorial resolution in all dimensions. Based on a series of lectures at Princeton University and written in an informal yet lucid style, this book is aimed at readers who are interested in both the historical roots of the modern methods and in a simple and transparent proof of this important theorem.
Resolution Of Curve And Surface Singularities In Characteristic Zero
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Author : K. Kiyek
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-11
Resolution Of Curve And Surface Singularities In Characteristic Zero written by K. Kiyek 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 2012-09-11 with Mathematics categories.
The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.
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.