Cepheid distances based on Gaia and VMC@VISTA observations

Abstract: We present new accurate Period-Luminosity (PL) and Period-Wesenheit (PW) relations in the V,J,Ks bands based on a sample of more than 4500 Cepheids in the Large Magellanic Cloud (LMC) whose photometry was obtained in the context of the VISTA Magellanic Clouds (VMC) Survey. The excellent precision of these data allows us to study the geometry of the LMC and to establish a solid baseline for extra-galactic distance scale studies. To calibrate the zero points of these PL/PW relations, we adopted Gaia Data Release 2 parallaxes for more than 2000 Milky Way Cepheids. The implications for the measurement of $H_0$ are briefly discussed.