The first spectroscopic census of AGNs associated to late-type galaxies in the Virgo cluster is carried on by observing 213 out of a complete set of 237 galaxies more massive than M_dyn>10^{8.5} solar masses. Among them, 77 are classified as AGNs (including 21 transition objects, 47 LINERs and 9 Seyferts), and comprize 32% of the late-type galaxies in Virgo. Due to spectroscopic incompleteness at most 21 AGNs are missed in the survey, so that the fraction would increase up to 41%. Using corollary Near-IR observations, that enable us to estimate galaxies dynamical masses, it is found that AGNs are hosted exclusively in massive galaxies, i.e. M_dyngsim 10^{10} solar masses. Their frequency increases steeply with the dynamical mass from zero at M_dynapprox10^{9.5} solar masses to virtually 1 at M_dyn>10^{11.5} solar masses. These frequencies are consistent with the ones of low luminosity AGNs found in the general field by the SDSS. Massive galaxies that harbor AGNs commonly show conspicuous r-band star-like nuclear enhancements. Conversely they often, but not necessarily contain massive bulges. Few well known AGNs (e.g. M61, M100, NGC4535) are found in massive Sc galaxies with little or no bulge. The AGN fraction seems to be only marginally sensitive to galaxy environment. We infer the black hole masses using the known scaling relations of quiescent black holes. No black holes lighter than $sim 10^6$ msol are found active in our sample.
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