The Grassmannian Variety

Author : V. Lakshmibai
Publisher :
ISBN 13 : 9781493930838
Total Pages : pages
Book Rating : 4.34/5 ( download)

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Download or read book The Grassmannian Variety written by V. Lakshmibai and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this text uniquely presents an exciting playing field for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen-Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. This text would serve well as a reference book for a graduate work on Grassmannian varieties and would be an excellent supplementary text for several courses including those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric and differential topology, representation theory of compact and reductive groups, Lie theory, toric varieties, geometric representation theory, and singularity theory. The reader should have some familiarity with commutative algebra and algebraic geometry.

Author : V. Lakshmibai
Publisher : Springer
ISBN 13 : 1493930826
Total Pages : 174 pages
Book Rating : 4.21/5 ( download)

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Download or read book The Grassmannian Variety written by V. Lakshmibai and published by Springer. This book was released on 2015-09-25 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this text uniquely presents an exciting playing field for graduate students and researchers in mathematics, physics, and computer science, to expand their knowledge in the field of algebraic geometry. The standard monomial theory (SMT) for the Grassmannian varieties and their Schubert subvarieties are introduced and the text presents some important applications of SMT including the Cohen–Macaulay property, normality, unique factoriality, Gorenstein property, singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. This text would serve well as a reference book for a graduate work on Grassmannian varieties and would be an excellent supplementary text for several courses including those in geometry of spherical varieties, Schubert varieties, advanced topics in geometric and differential topology, representation theory of compact and reductive groups, Lie theory, toric varieties, geometric representation theory, and singularity theory. The reader should have some familiarity with commutative algebra and algebraic geometry.

Author : Jerzy Weyman
Publisher : Cambridge University Press
ISBN 13 : 9780521621977
Total Pages : 404 pages
Book Rating : 4.76/5 ( download)

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Download or read book Cohomology of Vector Bundles and Syzygies written by Jerzy Weyman and published by Cambridge University Press. This book was released on 2003-06-09 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is an exposition of the geometric technique of calculating syzygies. It is written from a point of view of commutative algebra, and without assuming any knowledge of representation theory the calculation of syzygies of determinantal varieties is explained. The starting point is a definition of Schur functors, and these are discussed from both an algebraic and geometric point of view. Then a chapter on various versions of Bott's Theorem leads on to a careful explanation of the technique itself, based on a description of the direct image of a Koszul complex. Applications to determinantal varieties follow, plus there are also chapters on applications of the technique to rank varieties for symmetric and skew symmetric tensors of arbitrary degree, closures of conjugacy classes of nilpotent matrices, discriminants and resultants. Numerous exercises are included to give the reader insight into how to apply this important method.

Author : V Lakshmibai
Publisher : Springer
ISBN 13 : 9811313938
Total Pages : 312 pages
Book Rating : 4.36/5 ( download)

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Download or read book Flag Varieties written by V Lakshmibai and published by Springer. This book was released on 2018-06-26 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the importance of flag varieties in geometric objects and elucidates its richness as interplay of geometry, combinatorics and representation theory. The book presents a discussion on the representation theory of complex semisimple Lie algebras, as well as the representation theory of semisimple algebraic groups. In addition, the book also discusses the representation theory of symmetric groups. In the area of algebraic geometry, the book gives a detailed account of the Grassmannian varieties, flag varieties, and their Schubert subvarieties. Many of the geometric results admit elegant combinatorial description because of the root system connections, a typical example being the description of the singular locus of a Schubert variety. This discussion is carried out as a consequence of standard monomial theory. Consequently, this book includes standard monomial theory and some important applications—singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory. The two recent results on Schubert varieties in the Grassmannian have also been included in this book. The first result gives a free resolution of certain Schubert singularities. The second result is about certain Levi subgroup actions on Schubert varieties in the Grassmannian and derives some interesting geometric and representation-theoretic consequences.

Author : Robert Osserman
Publisher :
ISBN 13 :
Total Pages : 108 pages
Book Rating : 4.20/5 ( download)

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Download or read book Grassmannian Varieties written by Robert Osserman and published by . This book was released on 1950 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manuscript minor thesis in mathematics.

Author : Marek Golasiński
Publisher : Springer Nature
ISBN 13 : 3031364058
Total Pages : 342 pages
Book Rating : 4.51/5 ( download)

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Download or read book Grassmann and Stiefel Varieties over Composition Algebras written by Marek Golasiński and published by Springer Nature. This book was released on 2023-09-17 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with matrix manifolds, i.e., manifolds for which there is a natural representation of their elements as matrix arrays. Classical matrix manifolds (Stiefel, Grassmann and flag manifolds) are studied in a more general setting. It provides tools to investigate matrix varieties over Pythagorean formally real fields. The presentation of the book is reasonably self-contained. It contains a number of nontrivial results on matrix manifolds useful for people working not only in differential geometry and Riemannian geometry but in other areas of mathematics as well. It is also designed to be readable by a graduate student who has taken introductory courses in algebraic and differential geometry.

Author : Joe Harris
Publisher : Springer Science & Business Media
ISBN 13 : 1475721897
Total Pages : 344 pages
Book Rating : 4.98/5 ( download)

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Download or read book Algebraic Geometry written by Joe Harris and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship." --MATHEMATICAL REVIEWS

Author : Mauro Beltrametti
Publisher : European Mathematical Society
ISBN 13 : 9783037190647
Total Pages : 512 pages
Book Rating : 4.47/5 ( download)

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Download or read book Lectures on Curves, Surfaces and Projective Varieties written by Mauro Beltrametti and published by European Mathematical Society. This book was released on 2009 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions. The text is aimed at students in the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses at the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed. The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature.

Author : Ratko Darda
Publisher :
ISBN 13 :
Total Pages : 68 pages
Book Rating : 4.43/5 ( download)

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Download or read book Varieties, Grassmannian Varieties and Irreducibility written by Ratko Darda and published by . This book was released on 2015 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Piotr Pragacz
Publisher : Springer Science & Business Media
ISBN 13 : 3764373423
Total Pages : 321 pages
Book Rating : 4.29/5 ( download)

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Download or read book Topics in Cohomological Studies of Algebraic Varieties written by Piotr Pragacz and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume study various cohomological aspects of algebraic varieties: - characteristic classes of singular varieties; - geometry of flag varieties; - cohomological computations for homogeneous spaces; - K-theory of algebraic varieties; - quantum cohomology and Gromov-Witten theory. The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before. Contributors: Paolo Aluffi Michel Brion Anders Skovsted Buch Haibao Duan Ali Ulas Ozgur Kisisel Piotr Pragacz Jörg Schürmann Marek Szyjewski Harry Tamvakis