This article belongs to the first series of XXL publications. It presents
multifibre spectroscopic observations of three 0.55 sq.deg. fields in the XXL
Survey, which were selected on the basis of their high density of
X-ray-detected clusters. The observations were obtained with the
AutoFib2+WYFFOS (AF2) wide-field fibre spectrograph mounted on the 4.2m William
Herschel Telescope. The paper first describes the scientific rationale, the
preparation, the data reduction, and the results of the observations, and then
presents a study of active galactic nuclei (AGN) within three superclusters. We
obtained redshifts for 455 galaxies in total, 56 of which are counterparts of
X-ray point-like sources. We were able to determine the redshift of the merging
supercluster XLSSC-e, which consists of six individual clusters at z~0.43, and
we confirmed the redshift of supercluster XLSSC-d at z~0.3. More importantly,
we discovered a new supercluster, XLSSC-f, that comprises three galaxy clusters
also at z~0.3. We find a significant 2D overdensity of X-ray point-like sources
only around the supercluster XLSSC-f. This result is also supported by the
spatial (3D) analysis of XLSSC-f, where we find four AGN with compatible
spectroscopic redshifts and possibly one more with compatible photometric
redshift. In addition, we find two AGN (3D analysis) at the redshift of
XLSSC-e, but no AGN in XLSSC-d. Comparing these findings with the optical
galaxy overdensity we conclude that the total number of AGN in the area of the
three superclusters significantly exceeds the field expectations. The
difference in the AGN frequency between the three superclusters cannot be
explained by the present study because of small number statistics. Further
analysis of a larger number of superclusters within the 50 sq. deg. of the XXL
is needed before any conclusions on the effect of the supercluster environment
on AGN can be reached.Comment: 11 pages, published by A&