Surveys Of Modern Mathematics
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Surveys In Modern Mathematics
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Author : Viktor Vasilʹevich Prasolov
language : en
Publisher: Cambridge University Press
Release Date : 2005-04-14
Surveys In Modern Mathematics written by Viktor Vasilʹevich Prasolov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-14 with Mathematics categories.
Topics covered range from computational complexity, algebraic geometry, dynamics, through to number theory and quantum groups.
Surveys In Contemporary Mathematics
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Author : Nicholas Young
language : en
Publisher: Cambridge University Press
Release Date : 2008
Surveys In Contemporary Mathematics written by Nicholas Young and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Education categories.
A collection of articles showcasing the achievements of young Russian researchers in combinatorial and algebraic geometry and topology.
Open Problems And Surveys Of Contemporary Mathematics
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Author : Lizhen Ji
language : en
Publisher:
Release Date : 2013
Open Problems And Surveys Of Contemporary Mathematics written by Lizhen Ji and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Geometry, Differential categories.
Surveys Of Modern Mathematics
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Author :
language : en
Publisher:
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Surveys Of Modern 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 with categories.
N Ron Models
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Author : Siegfried Bosch
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
N Ron Models written by Siegfried Bosch 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.
Néron models were invented by A. Néron in the early 1960s in order to study the integral structure of abelian varieties over number fields. Since then, arithmeticians and algebraic geometers have applied the theory of Néron models with great success. Quite recently, new developments in arithmetic algebraic geometry have prompted a desire to understand more about Néron models, and even to go back to the basics of their construction. The authors have taken this as their incentive to present a comprehensive treatment of Néron models. This volume of the renowned "Ergebnisse" series provides a detailed demonstration of the construction of Néron models from the point of view of Grothendieck's algebraic geometry. In the second part of the book the relationship between Néron models and the relative Picard functor in the case of Jacobian varieties is explained. The authors helpfully remind the reader of some important standard techniques of algebraic geometry. A special chapter surveys the theory of the Picard functor.
Degeneration Of Abelian Varieties
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Author : Gerd Faltings
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Degeneration Of Abelian Varieties written by Gerd Faltings 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 2013-04-17 with Mathematics categories.
The topic of this book is the theory of degenerations of abelian varieties and its application to the construction of compactifications of moduli spaces of abelian varieties. These compactifications have applications to diophantine problems and, of course, are also interesting in their own right. Degenerations of abelian varieties are given by maps G - S with S an irre ducible scheme and G a group variety whose generic fibre is an abelian variety. One would like to classify such objects, which, however, is a hopeless task in this generality. But for more specialized families we can obtain more: The most important theorem about degenerations is the stable reduction theorem, which gives some evidence that for questions of compactification it suffices to study semi-abelian families; that is, we may assume that G is smooth and flat over S, with fibres which are connected extensions of abelian varieties by tori. A further assumption will be that the base S is normal, which makes such semi-abelian families extremely well behaved. In these circumstances, we give a rather com plete classification in case S is the spectrum of a complete local ring, and for general S we can still say a good deal. For a complete base S = Spec(R) (R a complete and normal local domain) the main result about degenerations says roughly that G is (in some sense) a quotient of a covering G by a group of periods.
Projective Differential Geometry Old And New
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Author : V. Ovsienko
language : en
Publisher: Cambridge University Press
Release Date : 2004-12-13
Projective Differential Geometry Old And New written by V. Ovsienko and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-13 with Mathematics categories.
Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. The authors' main goal in this 2005 book is to emphasize connections between classical projective differential geometry and contemporary mathematics and mathematical physics. They also give results and proofs of classic theorems. Exercises play a prominent role: historical and cultural comments set the basic notions in a broader context. The book opens by discussing the Schwarzian derivative and its connection to the Virasoro algebra. One-dimensional projective differential geometry features strongly. Related topics include differential operators, the cohomology of the group of diffeomorphisms of the circle, and the classical four-vertex theorem. The classical theory of projective hypersurfaces is surveyed and related to some very recent results and conjectures. A final chapter considers various versions of multi-dimensional Schwarzian derivative. In sum, here is a rapid route for graduate students and researchers to the frontiers of current research in this evergreen subject.
Rational Curves On Algebraic Varieties
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Author : Janos Kollar
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-06-22
Rational Curves On Algebraic Varieties written by Janos Kollar 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 1999-06-22 with Mathematics categories.
The aim of this book is to provide an introduction to the structure theory of higher dimensional algebraic varieties by studying the geometry of curves, especially rational curves, on varieties. The main applications are in the study of Fano varieties and of related varieties with lots of rational curves on them. This Ergebnisse volume provides the first systematic introduction to this field of study. The book contains a large number of examples and exercises which serve to illustrate the range of the methods and also lead to many open questions of current research.
Towards The Mathematics Of Quantum Field Theory
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Author : Frédéric Paugam
language : en
Publisher: Springer
Release Date : 2016-08-23
Towards The Mathematics Of Quantum Field Theory written by Frédéric Paugam and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-23 with Science categories.
This ambitious and original book sets out to introduce to mathematicians (even including graduate students ) the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in use. This in turn promotes the interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, though mathematicians are the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second part presents a large family of examples of classical field theories, both from experimental and theoretical physics, while the third part provides an introduction to quantum field theory, presents various renormalization methods, and discusses the quantization of factorization algebras.