Buildings and Schubert Schemes

A book in which algebra and algebraic geometry, combinatorics, and group theory interact in unusual and deep ways, this book discusses buildings and Schubert schemes. The first part of the book introduces Schubert cells and varieties of the general linear group GL(k^(r+1)) over a field k according to Ehresmann’s theorem. Smooth resolutions for these varieties are constructed in terms of Flag configurations ink^(r+1) given by linear graphs called minimal galleries. The second part focuses on Schubert schemes, the universal Schubert scheme, and their canonical smooth resolution in terms of the incidence relation in a relative building, which are constructed for a reductive group scheme.