  We use the GALEX data of the GUViCS survey to construct the NUV luminosity
function of the Virgo cluster over ~ 300 deg.2, an area covering the cluster
and its surrounding regions up to ~ 1.8 virial radii. The NUV luminosity
function is also determined for galaxies of different morphological type and
NUV-i colour, and for the different substructures within the cluster. These
luminosity functions are robust vs. statistical corrections since based on a
sample of 833 galaxies mainly identified as cluster members with spectroscopic
redshift (808) or high-quality optical scaling relations (10). We fit these
luminosity functions with a Schechter function, and compare the fitted
parameters with those determined for other nearby clusters and for the field.
The faint end slope of the Virgo NUV luminosity function (alpha = -1.19), here
sampled down to ~ NUV = -11.5 mag, is significantly flatter than the one
measured in other nearby clusters and similar to the field one. Similarly M* =
-17.56 is one-to-two magnitudes fainter than measured in Coma, A1367, the
Shapley supercluster, and the field. These differences seem due to the quite
uncertain statistical corrections and the small range in absolute magnitude
sampled in these clusters. We do not observe strong systematic differences in
the overall NUV luminosity function of the core of the cluster with respect to
that of its periphery. We notice, however, that the relative contribution of
red-to-blue galaxies at the faint end is inverted, with red quiescent objects
dominating the core of the cluster and star forming galaxies dominating beyond
one virial radius. These observational evidences are discussed in the framework
of galaxy evolution in dense environments.
