Going on a transtlantic cruise which arrives at 10 am in Genoa, how much time do I have if I am going on a 10:52 train to Rome. Will I have time to drop my suitcase at a downtown hotel and go to the train to catch the scheduled one ?
or do I take a later train

I would look into taking a later train. If the schedule states arriving at 10:00 am that means it could take a little time to get off the ship. Usually takes a couple hours to disembark the ship after arrival at a port.