  We analyze the influence of the dimensionality on the Cu 2p_3/2 core level
X-ray photoemission spectra of undoped cuprates. Both exchange splitting and
delocalization properties are described within one framework using a multi-band
Hubbard model. The spectral intensity is calculated by means of the
Mori-Zwanzig projection technique for a CuO_4 plaquette ('zero'-dimensional),
an infinite CuO_3 chain (one-dimensional), and an infinite CuO_2 plane
(two-dimensional). The results are compared to the spectra of Bi_2CuO_4,
Sr_2CuO_3, and Sr_2CuO_2Cl_2. Our analysis allows to distinguish between
effects of the Cu-O geometry and effects from material-specific properties.
