Abstract
Aag domain D = G=V forG a simple real non-compact groupG with compact Cartan subgroup is non-classical if it does not ber holomorphically or anti-holomorphically over a Hermitian symmetric space. We prove that for an innite, nitely generated discrete subgroup of G, the analytic space nD does not have an algebraic structure. We also give another proof of the theorem of Huckleberry that any two points in a non-classical domain D can be joined by a nite chain of compact subvarieties of D.
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