Connected components of closed affine Deligne-Lusztig varieties

Details Connected components of closed affine Deligne-Lusztig varieties Connected components of closed affine Deligne-Lusztig varieties

2006-07-26

arxiv.org/abs/math/0607678v2

Mathematics

Algebraic Geometry

15 pages, some errors corrected, to appear in Mathematische Annalen

Scientific paper

We determine the set of connected components of closed affine Deligne-Lusztig varieties for special maximal compact subgroups of split connected reductive groups. Especially, we show that such an affine Deligne-Lusztig variety has isolated points if and only if its dimension is 0. From the dimension formula for affine Deligne-Lusztig varieties we obtain a description of the set of these varieties that are zero-dimensional.

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