Classification Theory Of Polarized Varieties
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Classification Theories Of Polarized Varieties
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Author : Takao Fujita
language : en
Publisher: Cambridge University Press
Release Date : 1990
Classification Theories Of Polarized Varieties written by Takao Fujita 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 1990 with Mathematics categories.
A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarised higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or sur.
Classification Theory Of Polarized Varieties
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Author : Takao Fujita
language : en
Publisher: Cambridge University Press
Release Date : 1990-08-23
Classification Theory Of Polarized Varieties written by Takao Fujita 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 1990-08-23 with Mathematics categories.
Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarized higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or surveyed. Proofs are given in full in the central part of the development, but background and technical results are sometimes sketched in when the details are not essential for understanding the key ideas.
Moduli Theory And Classification Theory Of Algebraic Varieties
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Author : H. Popp
language : en
Publisher: Springer
Release Date : 2006-11-15
Moduli Theory And Classification Theory Of Algebraic Varieties written by H. Popp 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.
On The Geometry Of Some Special Projective Varieties
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Author : Francesco Russo
language : en
Publisher: Springer
Release Date : 2016-01-25
On The Geometry Of Some Special Projective Varieties written by Francesco Russo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-25 with Mathematics categories.
Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces, their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases. It also provides a solution of Hartshorne’s Conjecture on Complete Intersections for the class of quadratic manifolds and new short proofs of previously known results, using the modern tools of Mori Theory and of rationally connected manifolds. The new approach to some of the problems considered can be resumed in the principle that, instead of studying a special embedded manifold uniruled by lines, one passes to analyze the original geometrical property on the manifold of lines passing through a general point and contained in the manifold. Once this embedded manifold, usually of lower codimension, is classified, one tries to reconstruct the original manifold, following a principle appearing also in other areas of geometry such as projective differential geometry or complex geometry.
Rational Curves On Algebraic Varieties
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Author : Janos Kollar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
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 2013-04-09 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.
Projective Varieties With Unexpected Properties
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Author : Ciro Ciliberto
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22
Projective Varieties With Unexpected Properties written by Ciro Ciliberto and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.
This volume contains refereed papers related to the lectures and talks given at a conference held in Siena (Italy) in June 2004. Also included are research papers that grew out of discussions among the participants and their collaborators. All the papers are research papers, but some of them also contain expository sections which aim to update the state of the art on the classical subject of special projective varieties and their applications and new trends like phylogenetic algebraic geometry. The topic of secant varieties and the classification of defective varieties is central and ubiquitous in this volume. Besides the intrinsic interest of the subject, it turns out that it is also relevant in other fields of mathematics like expressions of polynomials as sums of powers, polynomial interpolation, rank tensor computations, Bayesian networks, algebraic statistics and number theory.
Character Theory For The Odd Order Theorem
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Author : Thomas Peterfalvi
language : en
Publisher: Cambridge University Press
Release Date : 2000-02-28
Character Theory For The Odd Order Theorem written by Thomas Peterfalvi 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 2000-02-28 with Mathematics categories.
The famous and important theorem of W. Feit and J. G. Thompson states that every group of odd order is solvable, and the proof of this has roughly two parts. The first part appeared in Bender and Glauberman's Local Analysis for the Odd Order Theorem which was number 188 in this series. This book provides the character-theoretic second part and thus completes the proof. All researchers in group theory should have a copy of this book in their library.
Discrete And Continuous Nonlinear Schr Dinger Systems
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Author : M. J. Ablowitz
language : en
Publisher: Cambridge University Press
Release Date : 2004
Discrete And Continuous Nonlinear Schr Dinger Systems written by M. J. Ablowitz 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 with Mathematics categories.
In recent years there have been important and far reaching developments in the study of nonlinear waves and a class of nonlinear wave equations which arise frequently in applications. The wide interest in this field comes from the understanding of special waves called 'solitons' and the associated development of a method of solution to a class of nonlinear wave equations termed the inverse scattering transform (IST). Before these developments, very little was known about the solutions to such 'soliton equations'. The IST technique applies to both continuous and discrete nonlinear Schrödinger equations of scalar and vector type. Also included is the IST for the Toda lattice and nonlinear ladder network, which are well-known discrete systems. This book, first published in 2003, presents the detailed mathematical analysis of the scattering theory; soliton solutions are obtained and soliton interactions, both scalar and vector, are analyzed. Much of the material is not available in the previously-published literature.
Corings And Comodules
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Author : Tomasz Brzezinski
language : en
Publisher: Cambridge University Press
Release Date : 2003-09-15
Corings And Comodules written by Tomasz Brzezinski 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 2003-09-15 with Mathematics categories.
This is the first extensive treatment of the theory of corings and their comodules. In the first part, the module-theoretic aspects of coalgebras over commutative rings are described. Corings are then defined as coalgebras over non-commutative rings. Topics covered include module-theoretic aspects of corings, such as the relation of comodules to special subcategories of the category of modules (sigma-type categories), connections between corings and extensions of rings, properties of new examples of corings associated to entwining structures, generalisations of bialgebras such as bialgebroids and weak bialgebras, and the appearance of corings in non-commutative geometry.
Second Order Partial Differential Equations In Hilbert Spaces
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Author : Giuseppe Da Prato
language : en
Publisher: Cambridge University Press
Release Date : 2002-07-25
Second Order Partial Differential Equations In Hilbert Spaces written by Giuseppe Da Prato 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 2002-07-25 with Mathematics categories.
Second order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterparts are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is then a discussion of how the results in the book can be applied to control theory. This area is developing very rapidly and there are numerous notes and references that point the reader to more specialised results not covered in the book. Coverage of some essential background material will help make the book self-contained and increase its appeal to those entering the subject.