  We determine the Hilbert-Kunz function of plane elliptic curves in odd
characteristic, as well as over arbitrary fields the generalized Hilbert-Kunz
functions of nodal cubic curves. Together with results of K. Pardue and P.
Monsky, this completes the list of Hilbert-Kunz functions of plane cubics.
Combining these results with the calculation of the (generalized) Hilbert-Kunz
function of Cayley's cubic surface, it follows that in each degree and over any
field of positive characteristic there are curves resp. surfaces taking on the
minimally possible Hilbert-Kunz multiplicity.
