  An edge-on debris disk was detected in 2015 around the young, nearby A0V star
HD 110058. The disk showed features resembling those seen in the disk of beta
Pictoris that could indicate the presence of a perturbing planetary-mass
companion in the system. We investigated new and archival scattered light
images of the disk in order to characterise its morphology and spectrum. In
particular, we analysed the disk's warp to constrain the properties of possible
planetary perturbers. Our work uses data from two VLT/SPHERE observations and
archival data from HST/STIS. We measured the morphology of the disk by
analysing vertical profiles along the length of the disk to extract the
centroid spine position and vertical height. We extracted the surface
brightness and reflectance spectrum of the disk. We detect the disk between 20
au (with SPHERE) and 150 au (with STIS), at a position angle of
159.6$^\circ\pm$0.6$^\circ$. Analysis of the spine shows an asymmetry between
the two sides of the disk, with a 3.4$^\circ\pm$0.9$^\circ$ warp between ~20 au
and 60 au. The disk is marginally vertically resolved in scattered light, with
a vertical aspect ratio of 9.3$\pm$0.7% at 45 au. The extracted reflectance
spectrum is featureless, flat between 0.95 micron and 1.1 micron, and red from
1.1 micron to 1.65 micron. The outer parts of the disk are also asymmetric with
a tilt between the two sides compatible with a disk made of forward-scattering
particles and seen not perfectly edge-on, suggesting an inclination of
<84$^\circ$. The presence of an undetected planetary-mass companion on an
inclined orbit with respect to the disk could explain the warp. The
misalignment of the inner parts of the disk with respect to the outer disk
suggests a warp that has not yet propagated to the outer parts of the disk,
favouring the scenario of an inner perturber as the origin of the warp.
