  The late-B magnetic chemically peculiar star CU Vir is one of the fastest
rotators among the intermediate-mass stars with strong fossil magnetic fields.
It shows a prominent rotational modulation of the spectral energy distribution
and absorption line profiles due to chemical spots and exhibits a unique
strongly beamed variable radio emission. Little is known about the magnetic
field topology of CU Vir. In this study we aim to derive, for the first time,
detailed maps of the magnetic field distribution over the surface of this star.
We use high-resolution spectropolarimetric observations covering the entire
rotational period. These data are interpreted using a multi-line technique of
least-squares deconvolution (LSD) and a new Zeeman Doppler imaging code based
on detailed polarised radiative transfer modelling of the Stokes I and V LSD
profiles. This new magnetic inversion approach relies on the spectrum synthesis
calculations over the full wavelength range covered by observations and does
not assume that the LSD profiles behave as a single spectral line with mean
parameters. We present magnetic and chemical abundance maps derived from the Si
and Fe lines. Mean polarisation profiles of both elements reveal a significant
departure of the magnetic field topology of CU Vir from the commonly assumed
axisymmetric dipolar configuration. The field of CU Vir is dipolar-like, but
clearly non-axisymmetric, showing a large difference of the field strength
between the regions of opposite polarity. The main relative abundance depletion
features in both Si and Fe maps coincide with the weak-field region in the
magnetic map. Detailed information on the distorted dipolar magnetic field
topology of CU Vir provided by our study is essential for understanding
chemical spot formation, radio emission, and rotational period variation of
this star.
