The Resolution Of Singular Algebraic Varieties
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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).
Introduction To Singularities
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Author : Shihoko Ishii
language : en
Publisher: Springer
Release Date : 2014-11-19
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 2014-11-19 with Mathematics categories.
This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry 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. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. 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. Another example is that the moduli spaces of varieties have natural compactification, the boundaries of which correspond to singular varieties. 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-dim ensional 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.
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 : 2004-10
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 2004-10 with Mathematics categories.
This book covers the beautiful theory of resolutions of surface singularities in characteristic zero. The primary goal is to present in detail, and for the first time in one volume, two proofs for the existence of such resolutions. One construction was introduced by H.W.E. Jung, and another is due to O. Zariski. Jung's approach uses quasi-ordinary singularities and an explicit study of specific surfaces in affine three-space. In particular, a new proof of the Jung-Abhyankar theorem is given via ramification theory. Zariski's method, as presented, involves repeated normalisation and blowing up points. It also uses the uniformization of zero-dimensional valuations of function fields in two variables, for which a complete proof is given. Despite the intention to serve graduate students and researchers of Commutative Algebra and Algebraic Geometry, a basic knowledge on these topics is necessary only. This is obtained by a thorough introduction of the needed algebraic tools in the two appendices.
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.
Singularities Algebraic Geometry Commutative Algebra And Related Topics
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Author : Gert-Martin Greuel
language : en
Publisher: Springer
Release Date : 2018-09-18
Singularities Algebraic Geometry Commutative Algebra And Related Topics 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 2018-09-18 with Mathematics categories.
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.
Curves In Projective Space
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Author : Joe Harris
language : en
Publisher: Montréal : Presses de l'Université de Montréal
Release Date : 1982-01-01
Curves In Projective Space written by Joe Harris and has been published by Montréal : Presses de l'Université de Montréal this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-01-01 with Courbes algébriques categories.
The Resolution Of Singularities Of An Algebraic Variety Over A Field Of Characteristic Zero
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Author : Heisuke Hironaka
language : en
Publisher:
Release Date : 1963
The Resolution Of Singularities Of An Algebraic Variety Over A Field Of Characteristic Zero written by Heisuke Hironaka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Algebraic fields categories.
Arithmetic Geometry
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Author : G. Cornell
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Arithmetic Geometry written by G. Cornell 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.
This volume is the result of a (mainly) instructional conference on arithmetic geometry, held from July 30 through August 10, 1984 at the University of Connecticut in Storrs. This volume contains expanded versions of almost all the instructional lectures given during the conference. In addition to these expository lectures, this volume contains a translation into English of Falt ings' seminal paper which provided the inspiration for the conference. We thank Professor Faltings for his permission to publish the translation and Edward Shipz who did the translation. We thank all the people who spoke at the Storrs conference, both for helping to make it a successful meeting and enabling us to publish this volume. We would especially like to thank David Rohrlich, who delivered the lectures on height functions (Chapter VI) when the second editor was unavoidably detained. In addition to the editors, Michael Artin and John Tate served on the organizing committee for the conference and much of the success of the conference was due to them-our thanks go to them for their assistance. Finally, the conference was only made possible through generous grants from the Vaughn Foundation and the National Science Foundation.
Algebraic Geometry
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Author : Dan Abramovich
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Algebraic Geometry written by Dan Abramovich 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 2009 with Mathematics categories.
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.
Riemannian Holonomy Groups And Calibrated Geometry
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Author : Dominic D. Joyce
language : en
Publisher: OUP Oxford
Release Date : 2007-02-22
Riemannian Holonomy Groups And Calibrated Geometry written by Dominic D. Joyce and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-22 with Mathematics categories.
This graduate level text covers an exciting and active area of research at the crossroads of several different fields in Mathematics and Physics. In Mathematics it involves Differential Geometry, Complex Algebraic Geometry, Symplectic Geometry, and in Physics String Theory and Mirror Symmetry. Drawing extensively on the author's previous work, the text explains the advanced mathematics involved simply and clearly to both mathematicians and physicists. Starting with the basic geometry of connections, curvature, complex and Kähler structures suitable for beginning graduate students, the text covers seminal results such as Yau's proof of the Calabi Conjecture, and takes the reader all the way to the frontiers of current research in calibrated geometry, giving many open problems.