Carlos Contou-Carrere

Buildings and Schubert Schemes

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: CRC Press
• Seitenzahl: 464
• Erscheinungstermin: 31. März 2021
• Englisch
• Abmessung: 234mm x 156mm x 25mm
• Gewicht: 699g
• ISBN-13: 9780367782665
• ISBN-10: 0367782669
• Artikelnr.: 61210016

Autorenporträt

Contou-Carrere, Carlos

Inhaltsangabe

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.