2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150217We 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.LaTex 2e with Xy-pic v3.2 for commutative diagramsAlgebraic GeometryCommutative Algebra11C20, 13H15, 14H45text