Study of the effect of neutrino oscillation on the supernova neutrino signal with the LVD detector

We present an update of our previous study (astro-ph/0112312) on how $\nu$ oscillations affect the signal from a supernova core collapse observed in the LVD detector at LNGS. In this paper we use a recent, more precise determination of the cross section (astro-ph/0302055) to calculate the expected number of inverse beta decay events, we introduce in the simulation also the $\nu$-{\rm Fe} interactions, we include the Earth matter effects and, finally, we study also the inverted mass hierarchy case.