  We present our sixth work in a series dedicated to variability studies of
active galactic nuclei (AGN) based on the survey of the COSMOS field by the VLT
Survey Telescope (VST). Its 54 r-band visits over 3.3 yr and single-visit depth
of 24.6 r-band mag make this dataset a valuable scaled-down version that can
help forecast the performance of the Rubin Observatory Legacy Survey of Space
and Time (LSST). This work is centered on the analysis of the structure
function (SF) of VST-COSMOS AGN, investigating possible differences in its
shape and slope related to how the AGN were selected, and explores possible
connections between the ensemble variability of AGN and black-hole mass,
accretion rate, bolometric luminosity, redshift, and obscuration of the source.
Given its features, our dataset opens up the exploration of samples ~2 mag
fainter than most of the literature to date. We identify several samples of AGN
- 677 in total - obtained by a variety of selection techniques which partly
overlap. Our analysis compares results for the various samples. We split each
sample in two based on the median of the physical property of interest, and
analyze differences in the shape and slope of the SF, and possible causes.
While the shape of the SF does not change with depth, it is highly affected by
the type of AGN (unobscured/obscured) included in the sample. Where a linear
region can be identified, we find that the variability amplitude anticorrelates
with accretion rate and bolometric luminosity, consistent with previous
literature on the topic, while no dependence on black-hole mass emerges from
this study. With its longer baseline and denser and more regular sampling, the
LSST will allow an improved characterization of the SF and its dependencies on
the mentioned physical properties over much larger AGN samples.
