Abstract
Some equivariant compactifications of the quotients PGLrn+1/PGLr are constructed. Each one is decomposed into locally closed strata which are smooth, are indexed by the entire convex pavings of the simplex of dimension n and admit a modular interpretation deduced from that of the Grassmann varieties. Together, they form a simplicial scheme which “compactifies” the classifying simplicial scheme of PGLr consisting of all the quotients PGLrn+1/PGLr, n≥0.
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