  Hard X-rays observed in Active Galactic Nuclei (AGNs) are thought to
originate from the Comptonization of the optical/UV accretion disk photons in a
hot corona. Polarization studies of these photons can help to constrain the
corona geometry and the plasma properties. We have developed a ray-tracing code
that simulates the Comptonization of accretion disk photons in coronae of
arbitrary shape, and use it here to study the polarization of the X-ray
emission from wedge and spherical coronae. We study the predicted polarization
signatures for the fully relativistic and various approximate treatments of the
elemental Compton scattering processes. We furthermore use the code to evaluate
the impact of non-thermal electrons and cyclo-synchrotron photons on the
polarization properties. Finally, we model the NuSTAR observations of the
Seyfert I galaxy Mrk 335 and predict the associated polarization signal. Our
studies show that X-ray polarimetry missions such as NASA's Imaging X-ray
Polarimetry Explorer (IXPE) and the X-ray Imaging Polarimetry Explorer (XIPE)
proposed to ESA will provide valuable new information about the physical
properties of the plasma close to the event horizon of AGN black holes.
