  Recently, many authors have embraced the study of certain properties of
modules such as projectivity, injectivity and flatness from an alternative
point of view. This way, Durgun has introduced absolutely pure domains of
modules as a mean to gauge the extent of the flatness of any given module (so
not just to determine whether or not the module is flat). In this paper, we
develop a new treatment of the goemetric flatness in categories of sheaves
which shed more light on some of its various important aspects. Namely, in
terms of this new approach, some classical schemes are characterized, some new
results are established and also known ones are generalized.
