Abstract
We prove some consequences of an old unpublished connectivity result of Mumford. These mostly deal with the fundamental group of some (ramified) coverings of homogeneous spaces; for example, it is shown that the fundamental group of a complex projective irreducible normal variety which is a covering of a simple (in the sense of 2.2) homogeneous space V, of degree ≤dim (V), is isomorphic to π1 (V).
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Financé en partie par N.S.F. Grant DMS 94-00636 et le Projet Européen HCM «Algebraic Geometry in Europe» (AGE), Contrat CHRXCT-940557.
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Debarre, O. Sur un théorème de connexité de Mumford pour les espaces homogènes. Manuscripta Math 89, 407–425 (1996). https://doi.org/10.1007/BF02567526
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DOI: https://doi.org/10.1007/BF02567526