  The GALEX Ultraviolet Virgo Cluster Survey (GUViCS) is a complete blind
survey of the Virgo cluster covering about 40 sq. deg. in the far UV (FUV,
lambda_eff=1539A, Delta-lambda=442A) and about 120 sq. deg. in the near UV
(NUV, lambda_eff=2316A, Delta-lambda=1060A). The goal of the survey is to study
the ultraviolet (UV) properties of galaxies in a rich cluster environment,
spanning a wide luminosity range from giants to dwarfs, and regardless of prior
knowledge of their star formation activity. The UV data will be combined with
those in other bands (optical: NGVS; far-infrared - submm: HeViCS; HI: ALFALFA)
and with our multizone chemo-spectrophotometric models of galaxy evolution to
make a complete and exhaustive study of the effects of the environment on the
evolution of galaxies in high density regions. We present here the scientific
objectives of the survey, describing the observing strategy and briefly
discussing different data reduction techniques. Using UV data already in-hand
for the central 12 sq. deg. we determine the FUV and NUV luminosity functions
of the Virgo cluster core for all cluster members and separately for early- and
late-type galaxies and compare it to the one obtained in the field and other
nearby clusters (Coma, A1367). This analysis shows that the FUV and NUV
luminosity functions of the core of the Virgo clusters are flatter (alpha about
-1.1) than those determined in Coma and A1367. We discuss the possible origin
of this difference
