3 edition of **Schubert Varieties (Progress in Mathematics)** found in the catalog.

Schubert Varieties (Progress in Mathematics)

V. Lakshmibai

- 212 Want to read
- 0 Currently reading

Published
**February 2007**
by Birkhauser
.

Written in English

- Mathematics,
- Science/Mathematics,
- Algebraic Geometry,
- Theory Of Groups,
- Geometry - Algebraic,
- Mathematics / Algebra / General,
- combinatorics,
- commutative algebra,
- Group Theory

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 352 |

ID Numbers | |

Open Library | OL8074681M |

ISBN 10 | 081764153X |

ISBN 10 | 9780817641535 |

FROBENIUS SPLITTING FOR SCHUBERT VARIETIES 1 1. Introduction Motivation. Let Gbe a semi-simple algebraic group over an algebraically closed eld kwith xed Borel subgroup Bcontaining a maximal torus T. When khas characteristic 0, the Borel-Weil-Bott Theorem allows one to recover the representation theory of Gfrom the geometry of the ag. 1) You might want equations for the preimage of the Schubert variety in GL_n (i.e. the Schubert variety in Stiefel coordinates). Their closures in M_n are matrix Schubert varieties, and their equations are given by Fulton in a paper in Duke Math J. in (not entirely sure about the year).

Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, taken from a summer school in Thurnau, aim to give an introduction to these topics, and to describe lates progress on these problems. Singular Loci of Schubert Varieties | "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.

"Singular Loci of Schubert Varieties is a work at the crossroads of representation theory, algebraic geometry, and combinatorics. 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."--Jacket. The Schubert varieties defined by inclusions, originally introduced by Gasharov and Reiner, turn out to be an important subclass, and we further develop some of their combinatorics. Applications include formulas for Kostant polynomials and presentations of cohomology rings for lci Schubert varieties.

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Study Guide

Study Guide

Written by three of the world's leading mathematicians in algebraic geometry, group theory, and combinatorics, this excellent self-contained exposition on Schubert Varieties unfolds systematically, from relevant introductory material on commutative algebra and algebraic geometry.

First-rate text for a graduate course or for self-study. About this book 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.

Schubert Varieties, Equivariant Cohomology and Characteristic Classes: IMPANGA 15 Jaroslaw Buczynski, Mateusz Michalek, Elisa Postinghel MPANGA stands for the activities of Algebraic Geometers at the Institute of Mathematics, Polish Academy of Sciences, including one of the most important seminars in algebraic geometry in Poland.

Introduction to “Schubert varieties, equivariant cohomology and characteristicclasses, IMPANGA15 volume” Jarosław Buczynski´ 1, Mateusz Michałek2 and Elisa Postinghel The volume This volume is a conclusion of the activities of IMPANGA in the years –, whichcelebrated15yearsof its existencein It is a follow up to previousbooks.

Schubert varieties owe their name to Hermann Schubert, who in pub-lished his book on enumerative geometry [Schu]. At that time, several people, such as Grassmann, Giambelli, Pieri, Severi, and of course Schubert, were inter-ested in this sort of questions.

For instance, in [Schu, Example 1 of x4] Schubert asks How many lines in P3. The Shubert series is a unique set of books designed to build character through conflict for both children and adults.

Shubert demonstrates helpful ways for children to solve Schubert Varieties book, while Mrs. Bookbinder models Conscious Discipline strategies for adults. 1 Standard Monomial Theory for Graˇmann varieties Standard Monomial theory (abbreviated as SMT) is the central theme of this book.

We think that the classical case of Schubert varieties in the. Franz Peter Schubert (fränts pā´tər shōō´bərt), –, Austrian composer, one of the most gifted musicians of the 19th symphonic works represent the best legacy of the classical tradition, while his songs exemplify the height of romantic lyricism.

I would suggest Part III of Fulton's Young Tableaux book (of which you should skip Part I) as the best starting point for learning about Schubert varieties. One can get very far in this subject with a naive 19th century view of algebraic geometry, especially if one is willing to occasionally accept without proof a few foundational facts (for.

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 by: 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. Franz Schubert () was born in Vienna of immigrant parents. During his short life he produced an astonishing amount of music.

Symphonies, chamber music, opera, church music, and songs (more than of them) poured forth in profusion/5(5). Schubert Varieties Spring, Prof. Sara Billey Wednesday, Friday Loew Syllabus Summary:This course will introduce Schubert Varieties from a combinatorial point of view.

The course will build on the course taught this past fall by Monty McGovern, however, it is possible to take this class without having seen the first. The Schubert conditions were considered by H. Schubert in connection with enumeration problems for geometric objects with given incidence properties.

Hilbert's 15th problem concerns a foundation for the enumeration theory developed by Schubert (see [Kl]). Schubert Varieties by V.

Lakshmibai,available at Book Depository with free delivery worldwide. 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.

ordinary pattern avoidance, showing that the Schubert varieties not satisfying our condi-tions are not lci appears to require working with more general notions of pattern avoid-ance. The Schubert varieties de ned by inclusions, originally introduced by Gasharov and Reiner, turn out to be an important subclass, and we further develop some of their.

Schubert Varieties A Schubert variety is a member of a family of projective varieties which is deﬁned as the closure of some orbit under a group action in a homogeneous space G/H. Typical properties: • They are all Cohen-Macaulay, some are “mildly” singular. • They have a.

The Schubert varieties defined by inclusions, originally introduced by Gasharov and Reiner, turn out to be an important subclass, and we further develop some of their combinatorics. Applications include formulas for Kostant polynomials and presentations of cohomology rings for lci Schubert varieties.

Book Description. The first part of this book introduces the Schubert Cells and varieties of the general linear group Gl (k^(r+1)) over a field k according to Ehresmann geometric way. Smooth resolutions for these varieties are constructed in terms of Flag Configurations in k^(r+1) given by linear graphs called Minimal Galleries.

The articles circulate around a broad range of topics within algebraic geometry such as vector bundles, Schubert varieties, degeneracy loci, homogeneous spaces, equivariant cohomology, Thom polynomials, characteristic classes, symmetric functions and polynomials, and algebraic geometry in .The book also treats, in the last chapter, some other applications of standard monomial theory, e.g., to the study of certain naturally occurring affine algebraic varieties that, like determinantal varieties, can be realized as open parts of Schubert varieties.PDF | We provide several ingredients towards a generalization of the Littlewood-Richardson rule from Chow groups to algebraic cobordism.

In particular, | Find, read and cite all the research.