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Pavages des simplexes, schémas de graphes recollés et compactification des PGLrn+1/PGLr

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Inventiones mathematicae Aims and scope

Abstract.

Some equivariant compactifications of the quotients PGL r n +1/PGL r 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 PGL r consisting of all the quotients PGL r n +1/PGL r , n≥0.

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Authors and Affiliations

  1. Université de Paris-Sud, Mathématique, bât. 425, URA D0752 du CNRS, F-91405 Orsay Cedex, France, , , , , , FR

    L. Lafforgue

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  1. L. Lafforgue
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Oblatum 8-IV-1998 & 8-X-1998 / Published online: 28 January 1999

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Lafforgue, L. Pavages des simplexes, schémas de graphes recollés et compactification des PGLrn+1/PGLr. Invent math 136, 233–271 (1999). https://doi.org/10.1007/s002220050309

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  • DOI: https://doi.org/10.1007/s002220050309

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