1# Library to Find Best eBook for Read
Author : Anna B. Veit
Release : 2014
Genre : Mathematics
Kind : eBook
Book Rating : 358/5 ( reviews)
Book Synopsis Singular Loci of Schubert Varieties and of Rank Varieties. From Scratch by : Anna B. Veit
Download or read book Singular Loci of Schubert Varieties and of Rank Varieties. From Scratch written by Anna B. Veit. This book was released on 2014. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Sara Sarason
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 24X/5 ( reviews)
Book Synopsis Singular Loci of Schubert Varieties by : Sara Sarason
Download or read book Singular Loci of Schubert Varieties written by Sara Sarason. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: "Singular Loci of Schubert Varieties" is a unique work at the crossroads of representation theory, algebraic geometry, and combinatorics. Over the past 20 years, many research articles have been written on the subject in notable journals. In this work, Billey and Lakshmibai have recreated and restructured the various theories and approaches of those articles and present a clearer understanding of this important subdiscipline of Schubert varieties – namely singular loci. The main focus, therefore, is on the computations for the singular loci of Schubert varieties and corresponding tangent spaces. The methods used include standard monomial theory, the nil Hecke ring, and Kazhdan-Lusztig theory. New results are presented with sufficient examples to emphasize key points. A comprehensive bibliography, index, and tables – the latter not to be found elsewhere in the mathematics literature – round out this concise work. After a good introduction giving background material, the topics are presented in a systematic fashion to engage a wide readership of researchers and graduate students.
Author : V Lakshmibai
Release : 2018-06-26
Genre : Mathematics
Kind : eBook
Book Rating : 938/5 ( reviews)
Book Synopsis Flag Varieties by : V Lakshmibai
Download or read book Flag Varieties written by V Lakshmibai. This book was released on 2018-06-26. 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 : William Fulton
Release : 2006-11-13
Genre : Mathematics
Kind : eBook
Book Rating : 043/5 ( reviews)
Book Synopsis Schubert Varieties and Degeneracy Loci by : William Fulton
Download or read book Schubert Varieties and Degeneracy Loci written by William Fulton. This book was released on 2006-11-13. Available in PDF, EPUB and Kindle. Book excerpt: Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, from a summer school in Thurnau, aim to give an introduction to these topics, and to describe recent progress on these problems. There are interesting interactions with the algebra of symmetric functions and combinatorics, as well as the geometry of flag manifolds and intersection theory and algebraic geometry.
Author : Jaime Gutierrez
Release : 2015-01-20
Genre : Computers
Kind : eBook
Book Rating : 812/5 ( reviews)
Book Synopsis Computer Algebra and Polynomials by : Jaime Gutierrez
Download or read book Computer Algebra and Polynomials written by Jaime Gutierrez. This book was released on 2015-01-20. Available in PDF, EPUB and Kindle. Book excerpt: Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life. This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. Algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects. The papers presented were selected from the Workshop on Computer Algebra and Polynomials, which was held in Linz at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) during November 25-29, 2013, at the occasion of the Special Semester on Applications of Algebra and Number Theory.
