  We present a computational study of 2$p$ core-level X-ray photoemission
spectra of transition metal monoxides MO (M=Ni, Co, Mn) and sesquioxides
M$_2$O$_3$ (M=V, Cr, Fe) using a theoretical framework based on the
local-density approximation (LDA) $+$ dynamical mean-field theory (DMFT). We
find a very good description of the fine spectral features, which improves
considerably over the conventional cluster model. We analyze the role of the
non-local screening and its relationship to the long-range magnetic order and
the lattice geometry. Our results reveal the potential of the present method
for the analysis and interpretation of the modern high-energy-resolution
experiments.
