Tangents And Secants Of Algebraic Varieties
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Tangents And Secants Of Algebraic Varieties
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Author : F. L. Zak
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Tangents And Secants Of Algebraic Varieties written by F. L. Zak 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 1993 with Mathematics categories.
"The book is devoted to geometry of algebraic varieties in projective spaces. Among the objects considered in some detail are tangent and secant varieties, Gauss maps, dual varieties, hyperplane sections, projections, and varieties of small codimension. Emphasis is made on the study of interplay between irregular behavior of (higher) secant varieties and irregular tangencies to the original variety. Classification of varieties with unusual tangential properties yields interesting examples many of which arise as orbits of representations of algebraic groups."--ABSTRACT.
Tangents And Secants Of Algebraic Varieties
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Author : Francesco Russo
language : en
Publisher:
Release Date : 2003
Tangents And Secants Of Algebraic Varieties written by Francesco Russo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
Algebraic Transformation Groups And Algebraic Varieties
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Author : Vladimir Leonidovich Popov
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-04-01
Algebraic Transformation Groups And Algebraic Varieties written by Vladimir Leonidovich Popov 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 2004-04-01 with Mathematics categories.
The book covers topics in the theory of algebraic transformation groups and algebraic varieties which are very much at the frontier of mathematical research.
The Adjunction Theory Of Complex Projective Varieties
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Author : Mauro C. Beltrametti
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-03
The Adjunction Theory Of Complex Projective Varieties written by Mauro C. Beltrametti 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 2011-06-03 with Mathematics categories.
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
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.
Commutative Algebra
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Author : Irena Peeva
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-01
Commutative Algebra written by Irena Peeva 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 2013-02-01 with Mathematics categories.
This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, including core areas in Commutative Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit of junior mathematicians and researchers who are new to the field; it will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research.
Handbook Of Geometry And Topology Of Singularities Iv
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Author : José Luis Cisneros-Molina
language : en
Publisher: Springer Nature
Release Date : 2023-10-07
Handbook Of Geometry And Topology Of Singularities Iv written by José Luis Cisneros-Molina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-07 with Mathematics categories.
This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex. Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Surveys In Geometry And Number Theory
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Author : Nicholas Young
language : en
Publisher: Cambridge University Press
Release Date : 2007-01-18
Surveys In Geometry And Number Theory 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 2007-01-18 with Mathematics categories.
A collection of survey articles by leading young researchers, showcasing the vitality of Russian mathematics.
Problems And Theorems In Linear Algebra
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Author : Viktor Vasil_evich Prasolov
language : en
Publisher: American Mathematical Soc.
Release Date : 1994-06-13
Problems And Theorems In Linear Algebra written by Viktor Vasil_evich Prasolov 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 1994-06-13 with Mathematics categories.
There are a number of very good books available on linear algebra. However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many of these results and proofs obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks. In addition, more than a few interesting old results are not covered in many books. In this book, the author provides the basics of linear algebra, with an emphasis on new results and on nonstandard and interesting proofs. The book features about 230 problems with complete solutions. It can serve as a supplementary text for an undergraduate or graduate algebra course.
Projective Geometry And Formal Geometry
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Author : Lucian Badescu
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Projective Geometry And Formal Geometry written by Lucian Badescu 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 aim of this monograph is to introduce the reader to modern methods of projective geometry involving certain techniques of formal geometry. Some of these methods are illustrated in the first part through the proofs of a number of results of a rather classical flavor, involving in a crucial way the first infinitesimal neighbourhood of a given subvariety in an ambient variety. Motivated by the first part, in the second formal functions on the formal completion X/Y of X along a closed subvariety Y are studied, particularly the extension problem of formal functions to rational functions. The formal scheme X/Y, introduced to algebraic geometry by Zariski and Grothendieck in the 1950s, is an analogue of the concept of a tubular neighbourhood of a submanifold of a complex manifold. It is very well suited to study the given embedding Y\subset X. The deep relationship of formal geometry with the most important connectivity theorems in algebraic geometry, or with complex geometry, is also studied. Some of the formal methods are illustrated and applied to homogeneous spaces. The book contains a lot of results obtained over the last thirty years, many of which never appeared in a monograph or textbook. It addresses to algebraic geometers as well as to those interested in using methods of algebraic geometry.