Context : The GALEX Ultraviolet Virgo Cluster Survey ( GUViCS ) is a complete blind survey of the Virgo cluster covering \sim 40 sq .
deg .
in the far UV ( FUV , \lambda _ { eff } = 1539 \AA, \Delta \lambda = 442 \AA ) and \sim 120 sq .
deg .
in the near UV ( NUV , \lambda _ { eff } = 2316 \AA, \Delta \lambda = 1060 \AA ) .
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 \sim -1.1 ) than those determined in Coma and A1367 .
We discuss the possible origin of this difference .

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