Buildings and Schubert Schemes
Auteur : Contou-Carrere Carlos
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. In the second part, Schubert Schemes, the Universal Schubert Scheme and their Canonical Smooth Resolution, in terms of the incidence relation in a Tits relative building are constructed for a Reductive Group Scheme as in Grothendieck's SGAIII. This is a topic where algebra and algebraic geometry, combinatorics, and group theory interact in unusual and deep ways.
Grassmannians and Flag Varieties. Schubert Cell Decomposition of Grassmannians and Flag Varieties. Resolution of Singularities of a Schubert Variety. The Singular Locus of a Schubert Variety. The Flag Complex. Configurations and Galleries Varieties. Configurations Varieties as Galleries Varieties. The Coxeter Complex. Minimal Generalized Galleries in a Coxeter Complex. Minimal Generalized Galleries in a Reductive Group Building. Parabolic Subgroups in a Reductive Group Scheme. Associated Schemes to the Relative Building. Incidence Type Schemes of the Relative Building. Smooth Resolutions of Schubert Schemes. Contracted Products and Galleries Configurations Schemes. Functoriality of Schubert Schemes Smooth Resolutions and Base Changes. About the Coxeter Complex. Generators and Relations and the Building of a Reductive Group.
Date de parution : 03-2021
15.6x23.4 cm
Date de parution : 10-2016
15.6x23.4 cm
Thèmes de Buildings and Schubert Schemes :
Mots-clés :
Counter Clock Wise; Generalized Galleries; singular locus of a Schubert variety; Coxeter System; coxeter complex; Parabolic Subgroup; Tits building of a reductive group; Minimal Galleries; parabolics; Descent Data; reductive group scheme; Bruhat Decomposition; resolution of singularities; Bruhat's Lemma; smooth resolution; Fiber Decomposition; Smooth Resolution; Schubert Cell; Orbit Decomposition; Schubert Varieties; Schubert Schemes; Maximal Torus; Zariski's Tangent Space; Combinatorial Flags; Flag Varieties; Affine Open Sets; Convex Hull; Reductive Algebraic Group; Relative Position Matrices; Birational Morphism; Commutative Diagram; Parabolic Set; Affine Coordinates