Nilpotent orbits in small characteristic

We show that the number of nilpotent orbits in the dual of an exceptional Lie algebra is finite in bad characteristic. We determine the closure relations on the set of nilpotent orbits in the dual of classical and exceptional Lie algebras. Moreover for classical groups, we give an explicit description of the nilpotent pieces (which are unions of nilpotent orbits) in the dual defined in \cite{L4,X4}, in particular the definition of nilpotent pieces in \cite{L4,X4} coincides with the definition given by closure relations on nilpotent orbits.