  In the first part we extend the construction of the smooth normal-crossing
divisors compactification of projectivized strata of abelian differentials
given by Bainbridge, Chen, Gendron, Grushevsky and Moeller to the case of
k-differentials. Since the generalized construction is closely related to the
original one, we mainly survey their results and justify the details that need
to be adapted in the more general context.
  In the second part we show that the flat area provides a canonical hermitian
metric on the tautological bundle over the projectivized strata of finite area
k-differentials whose curvature form represents the first Chern class. This
result is useful in order to apply Chern-Weyl theory tools. It has already been
used as an assumption in the work of Sauvaget for abelian differentials and is
also used in a paper of Chen, M\"oller and Sauvaget for quadratic
differentials.
