Geodesic
A modular compactification of the general linear group
Documenta mathematica, Tome 5 (2000), pp. 553-594
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We define a certain compactifiction of the general linear group and give a modular description for its points with values in arbitrary schemes. This is a first step in the construction of a higher rank generalization of Gieseker's degeneration of moduli spaces of vector bundles over a curve. We show that our compactification has similar properties as the “wonderful compactification” of algebraic groups of adjoint type as studied by de Concini and Procesi. As a byproduct we obtain a modular description of the points of the wonderful compactification of PGln​.
DOI : 10.4171/dm/87
Classification : 14H60, 14M15
Mots-clés : moduli of vector bundles on curves, modular compactification, general linear group 
@article{10_4171_dm_87,
     author = {Ivan Kausz},
     title = {A modular compactification of the general linear group},
     journal = {Documenta mathematica},
     pages = {553--594},
     year = {2000},
     volume = {5},
     doi = {10.4171/dm/87},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/87/}
}
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Ivan Kausz. A modular compactification of the general linear group. Documenta mathematica, Tome 5 (2000), pp. 553-594. doi: 10.4171/dm/87

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