We examine supersymmetry of four-dimensional asymptotically anti-de Sitter
(AdS) dyonic black holes in the context of gauged N = 2 supergravity. Our c
alculations concentrate on black holes with unusual topology and their rota
ting generalizations, but we also reconsider the spherical rotating dyonic
Kerr-Newman-AdS black hole, whose supersymmetry properties have previously
been investigated by Kostelecky and Ferry within another approach. We find
that in the case of spherical, toroidal or cylindrical event horizon topolo
gy, the black holes must rotate in order to preserve some supersymmetry; th
e non-rotating supersymmetric configurations representing naked singulariti
es. However, we show that this is no more true for black holes whose event
horizons are Riemann surfaces of genus g > 1, where we find a non-rotating
extremal solitonic black hole carrying magnetic charge and permitting one K
illing spinor. For the non-rotating supersymmetric configurations of variou
s topologies, all Killing spinors are explicitly constructed. (C) 1999 Else
vier Science B.V.