MEROMORPHIC QUOTIENTS FOR SOME HOLOMORPHIC G-ACTIONS

Using mainly tools from previous articles we give necessary and sufficient conditions on the G-orbits' configuration in X in order that a holomorphic action of a connected complex Lie group G on a reduced complex space X admits a strongly quasi-proper meromorphic quotient. To show how these conditions can be used, we show, when G = K.B with B a closed connected complex subgroup of G and K a real compact subgroup of G, the existence of a strongly quasi-proper meromorphic quotient for the G-action on X, assuming a slightly stronger condition than the existence of such a quotient for the B-action. We also give a similar result when the connected complex Lie group has the form G = K.A.K where A is a closed connected complex subgroup and K is a compact (real) subgroup.