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Flag varieties

N. Gonciuela, V. Lakshmibai

332 pages, parution le 01/06/2001

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Résumé

Flag varieties constitute an important class of homogeneous spaces. Because of their rich geometry and combinatorics, they represent fundamental objects in the areas of Algebraic Geometry, Algebraic Groups and Representation Theory. This book provides an introduction to the subject, and presents the interplay of flag varieties among Geometry, Combinatorics and Representation Theory.

The Schubert subvarieties provide a powerful inductive machinery for the study of flag varieties. The central theme of this book is the theory of Schubert varieties - their geometric properties, ideal theory, singularity theory.

This book also presents the relationship between Schubert varieties and certain affine varieties - classical determinantal varieties, ladder determinantal varieties, quiver varieties. varieties of complexes, certain affine toric varieties.

This book includes a detailed treatment of the classical determinantal varieties, their normality, Cohen-Macaulayness, singular loci, relationship to classical invariant theory : the treatment uses their relationship to Schubert varieties.

Contents

Preliminaries.
Algebraic groups.
Generalities on G/B and G/Q.
Representations of semisimple algebraic groups.
The groups SL (n) and GL (n).
The Grassmannian variety Gd, n.
The flag variety.
Singularities of Schubert varieties.
Rational smoothness and Kazhdan-Lusztig theory.
Degenerations of Schubert varieties to toric varieties.
Some affine varieties related to Schubert varieties.
The cohomology and homology of the flag variety.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Hermann
Auteur(s)	N. Gonciuela, V. Lakshmibai
Parution	01/06/2001
Nb. de pages	332
Format	17 x 24
Couverture	Broché
Poids	631g
Intérieur	Noir et Blanc
EAN13	9782705663896
ISBN13	978-2-7056-6389-6