  We consider a thin superconducting film with a magnetic dot with permanent
magnetization (normal to the film) placed on it by a method based on
London-Maxwell equations. For sufficiently high dot magnetization a single
vortex appears in the ground state. Further increase of magnetization is
accompanied with the appearance of antivortices and more vortices in the film.
We study analytically conditions for the appearance of a vortex--antivortex
pair for a range of parameters. The phase diagram with diversity of
vortex--antivortex states is calculated numerically. When appear in the ground
state, antivortices are at distances comparable to the dot radius. For not too
large dot radii the total vorticity in the ground state is predominantly zero
or one. Magnetic field due to the dot and vortices everywhere in space is
calculated analytically.
