  X-ray polarimetry can potentially constrain the unknown geometrical shape of
AGN coronae. We present simulations of the X-ray polarization signal expected
from AGN coronae, assuming three different geometries, namely slab, spherical
and conical. We use the fully relativistic Monte-Carlo Comptonization code monk
to compute the X-ray polarization degree and angle. We explore different
coronal parameters such as shape, size, location and optical depth. Different
coronal geometries give a significantly different X-ray polarization signal. A
slab corona yields a high polarization degree, up to 14% depending on the
viewing inclination; a spherical corona yields low values, about 1-3%, while a
conical corona yields intermediate values. We also find a difference of 90
degrees in polarization angle between the slab corona and the spherical or
conical coronae. Upcoming X-ray polarimetry missions like IXPE will allow us to
observationally distinguish among different coronal geometries in AGNs for the
first time.
