I present an overview of our ongoing project aimed at building a new generation of velocity dispersion profiles ad rotation curves for a representative sample of Galactic globular clusters, from the the radial velocity of hundreds of individual stars distributed at different distances from the cluster center. The innermost portion of the profiles will be used to constrain the possible presence of intermediate-mass black holes. The adopted methodology consists of combining spectroscopic observations acquired with three different instruments at the ESO-VLT: the adaptive-optics assisted, integral field unit (IFU) spectrograph SINFONI for the innermost and highly crowded cluster cores, the multi-IFU spectrograph KMOS for the intermediate regions, and the multi-fiber instrument FLAMES/GIRAFFE-MEDUSA for the outskirts. The case of NGC 6388, representing the pilot project that motivated the entire program, is described in some details.

Eight cool giants in the unusual globular cluster NGC 6388 have been investigated in order to derive their elemental abundances. Average relative-to-solar abundance of iron is about –0.8. We have found that oxygen abundance is reduced as compared to most stars of a similar metallicity. The reduced carbon as compared to oxygen is at the level to be expected for red giant tip stars. Abundance of the rest of investigated elements are within the expected limits for the globular cluster stars.