Abstract: Catalyst systems for the polymerization of C.sub.2 -C.sub.10 -alkenes contain, as active components, a metallocene complex of a metal of subgroup IV or V of the Periodic Table, an oligomeric alumina compound and a cyclic boron compound of the general formula IV ##STR1## where R.sup.18 to R.sup.20 are each C.sub.1 -C.sub.10 -alkyl which may be monosubstituted to trisubstituted by halogen, C.sub.6 -C.sub.15 -aryl or C.sub.1 -C.sub.10 -alkoxy,C.sub.4 -C.sub.7 -cycloalkyl which may be monosubstituted to trisubstituted by halogen, C.sub.1 -C.sub.10 -alkyl or C.sub.1 -C.sub.10 -alkoxy,C.sub.1 -C.sub.10 -alkoxy which may be monosubstituted to trisubstituted by halogen, C.sub.1 -C.sub.10 -alkyl or C.sub.6 -C.sub.15 -aryl, or C.sub.6 -C.sub.15 -aryl which may be monosubstituted to pentasubstituted by halogen, C.sub.1 -C.sub.10 -alkyl or C.sub.1 -C.sub.10 -alkoxy.

Abstract: A process for the preparation of a supported catalyst for the polymerization of .alpha.-olefins, in which(1) a silicon dioxide-containing support gel is prepared by(1.1) introducing a sodium water glass or potassium water glass solution into a swirling stream of an aqueous mineral acid longitudinally and tangentially to the stream, spraying the resultant silica hydrosol in drop form into a gaseous medium and allowing it to solidify to form a hydrogel, and freeing the resultant hydrogel from salts by washing without prior ageing,(1.2) drying the hydrogel resulting from (1.1) to form the support gel,(2) the support gel (1) is charged with chromium trioxide or a chromium compound which can be converted into chromium trioxide under the conditions of process step (3), giving a chromium-containing support gel, and(3) the chromium-containing support gel (2) is heated at from 400.degree. to 1100.degree. C.

Abstract: Homopolymers of ethylene or copolymers of ethylene with minor amounts of other C.sub.3 -C.sub.12 -alk-1-enes are prepared by catalytic polymerization in a suspension or in the gas phase in the presence of an antistatic agent at from 50 to 120.degree. C. and from 5 to 50 bar by a process in which the antistatic agent used is a mixture of the following substances:a) a metal salt of medialanic acid of the formula (I) ##STR1## b) a metal salt of an anthranilic acid of the general formula (II) ##STR2## where the organic radical R.sup.1 is either.alpha.)--CO--(CH.sub.2).sub.x --CH.sub.3 (II.alpha.)or.beta.)--CO--(CH.sub.2).sub.y --CH.dbd.CH--(CH.sub.2).sub.z --CH.sub.3(III.beta.)and x, y and z are each an integer and are from 6 to 18 for x, from 1 to 16 for y, from 1 to 16 for z and from 4 to 17 for y+z, andc) a polyamine obtainable by reacting epichlorohydrin and an aliphatic primary monoamine or an N-alkylalkylenediamine of the general formula (IV)R.sup.2 NH--R.sup.3 --NH.sub.2 (IV),whereR.sup.2 is C.sub.8 -C.