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Buildings and Schubert Schemes

Carlos Contou-Carrere 1, *
* Corresponding author
Abstract : 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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https://hal.archives-ouvertes.fr/hal-01940773
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Submitted on : Friday, November 30, 2018 - 3:06:26 PM
Last modification on : Tuesday, November 5, 2019 - 5:14:37 PM

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  • HAL Id : hal-01940773, version 1

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Carlos Contou-Carrere. Buildings and Schubert Schemes. CRC Press, pp.462, 2016, 9781498768290. ⟨hal-01940773⟩

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