- 462 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
Buildings and Schubert Schemes
About this book
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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Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Buildings and Schubert Schemes by Carlos Contou-Carrere in PDF and/or ePUB format, as well as other popular books in Matemáticas & Conteo y numeración. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Cover
- Half Title
- Title Page
- Copyright Page
- Preface
- Table of Contents
- 1. Grassmannians and Flag Varieties
- 2. Schubert Cell Decomposition of Grassmannians and Flag Varieties
- 3. Resolution of Singularities of a Schubert Variety
- 4. The Singular Locus of a Schubert Variety
- 5. The Flag Complex
- 6. Configurations and Galleries varieties
- 7. Configuration Varieties as Gallery Varieties
- 8. The Coxeter complex
- 9. Minimal Generalized Galleries in a Coxeter Complex
- 10. Minimal Generalized Galleries in a Reductive Group Building
- 11. Parabolic Subgroups in a Reductive Group Scheme
- 12. Associated Schemes to the Relative Building
- 13. Incidence Type Schemes of the Relative Building
- 14. Smooth Resolutions of Schubert Schemes
- 15. Contracted Products and Galleries Configurations Schemes
- 16. Functoriality of Schubert Schemes Smooth Resolutions and Base Changes
- Appendix A: About the Coxeter Complex
- Appendix B: Generators and Relations and the Building of a Reductive Group
- References
- Index