Sur les quotients discrets de semi-groupes complexes

Details Sur les quotients discrets de semi-groupes complexes Sur les quotients discrets de semi-groupes complexes

2008-04-22

arxiv.org/abs/0804.3556v1

Ann. Fac. Sci. Toulouse Math. (6) 19 (2010), no. 2, 269-276

Mathematics

Complex Variables

6 pages, in french

Scientific paper

Let $X=G/K$ be an irreducible Hermitian symmetric space of the non-compact type and let $S\in G^\mbb{C}$ be the associated compression semi-group. Let $\Gamma$ be a discrete subgroup of $G$. We give a sufficient condition for $\Gamma\backslash S$ to be a Stein manifold. Moreover, we show that in general $\Gamma\backslash S$ is not Stein, which disproves a conjecture by Achab, Betten and Kr\"otz.

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