Desingularization Invariants And Strategy
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Desingularization Invariants And Strategy
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Author : Vincent Cossart
language : en
Publisher: Springer Nature
Release Date : 2020-08-27
Desingularization Invariants And Strategy written by Vincent Cossart and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-27 with Mathematics categories.
This book provides a rigorous and self-contained review of desingularization theory. Focusing on arbitrary dimensional schemes, it discusses the important concepts in full generality, complete with proofs, and includes an introduction to the basis of Hironaka’s Theory. The core of the book is a complete proof of desingularization of surfaces; despite being well-known, this result was no more than folklore for many years, with no existing references. Throughout the book there are numerous computations on standard bases, blowing ups and characteristic polyhedra, which will be a source of inspiration for experts exploring bigger dimensions. Beginners will also benefit from a section which presents some easily overlooked pathologies.
Desingularization Strategies Of Three Dimensional Vector Fields
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Author : Felipe Cano Torres
language : en
Publisher: Springer
Release Date : 2006-11-15
Desingularization Strategies Of Three Dimensional Vector Fields written by Felipe Cano Torres and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
For a vector field #3, where Ai are series in X, the algebraic multiplicity measures the singularity at the origin. In this research monograph several strategies are given to make the algebraic multiplicity of a three-dimensional vector field decrease, by means of permissible blowing-ups of the ambient space, i.e. transformations of the type xi=x'ix1, 2i
Lecture Notes In Mathematics
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Author :
language : en
Publisher:
Release Date : 1964
Lecture Notes In Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Mathematics categories.
Complex Analytic Desingularization
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Author : José Manuel Aroca
language : en
Publisher: Springer
Release Date : 2018-11-03
Complex Analytic Desingularization written by José Manuel Aroca and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-03 with Mathematics categories.
[From the foreword by B. Teissier] The main ideas of the proof of resolution of singularities of complex-analytic spaces presented here were developed by Heisuke Hironaka in the late 1960s and early 1970s. Since then, a number of proofs, all inspired by Hironaka's general approach, have appeared, the validity of some of them extending beyond the complex analytic case. The proof has now been so streamlined that, although it was seen 50 years ago as one of the most difficult proofs produced by mathematics, it can now be the subject of an advanced university course. Yet, far from being of historical interest only, this long-awaited book will be very rewarding for any mathematician interested in singularity theory. Rather than a proof of a canonical or algorithmic resolution of singularities, what is presented is in fact a masterly study of the infinitely near “worst” singular points of a complex analytic space obtained by successive “permissible” blowing ups and of the way to tame them using certain subspaces of the ambient space. This taming proves by an induction on the dimension that there exist finite sequences of permissible blowing ups at the end of which the worst infinitely near points have disappeared, and this is essentially enough to obtain resolution of singularities. Hironaka’s ideas for resolution of singularities appear here in a purified and geometric form, in part because of the need to overcome the globalization problems appearing in complex analytic geometry. In addition, the book contains an elegant presentation of all the prerequisites of complex analytic geometry, including basic definitions and theorems needed to follow the development of ideas and proofs. Its epilogue presents the use of similar ideas in the resolution of singularities of complex analytic foliations. This text will be particularly useful and interesting for readers of the younger generation who wish to understand one of the most fundamental results in algebraic and analytic geometry and invent possible extensions and applications of the methods created to prove it.
Desingularization Strategies For Three Dimensional Vector Fields
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Author :
language : pt-BR
Publisher:
Release Date : 1969
Desingularization Strategies For Three Dimensional Vector Fields written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.
Publicationes Mathematicae
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Author : Kossuth Lajos Tudományegyetem. Matematikai Intézet
language : en
Publisher:
Release Date : 1990
Publicationes Mathematicae written by Kossuth Lajos Tudományegyetem. Matematikai Intézet and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
Contact And Symplectic Topology
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Author : Frédéric Bourgeois
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-03-10
Contact And Symplectic Topology written by Frédéric Bourgeois 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 2014-03-10 with Science categories.
Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new research field worldwide. The intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.
Degenerate Relative Gromov Witten Invariants And Symplectic Sums
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Author : Joshua R. Davis
language : en
Publisher:
Release Date : 2005
Degenerate Relative Gromov Witten Invariants And Symplectic Sums written by Joshua R. Davis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Rational Points On Varieties
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Author : Bjorn Poonen
language : en
Publisher: American Mathematical Society
Release Date : 2023-08-10
Rational Points On Varieties written by Bjorn Poonen and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-10 with Mathematics categories.
This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere. The origins of arithmetic (or Diophantine) geometry can be traced back to antiquity, and it remains a lively and wide research domain up to our days. The book by Bjorn Poonen, a leading expert in the field, opens doors to this vast field for many readers with different experiences and backgrounds. It leads through various algebraic geometric constructions towards its central subject: obstructions to existence of rational points. —Yuri Manin, Max-Planck-Institute, Bonn It is clear that my mathematical life would have been very different if a book like this had been around at the time I was a student. —Hendrik Lenstra, University Leiden Understanding rational points on arbitrary algebraic varieties is the ultimate challenge. We have conjectures but few results. Poonen's book, with its mixture of basic constructions and openings into current research, will attract new generations to the Queen of Mathematics. —Jean-Louis Colliot-Thélène, Université Paris-Sud A beautiful subject, handled by a master. —Joseph Silverman, Brown University
Handbook Of Geometry And Topology Of Singularities Vi Foliations
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Author : Felipe Cano
language : en
Publisher: Springer Nature
Release Date :
Handbook Of Geometry And Topology Of Singularities Vi Foliations written by Felipe Cano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.