Hilbert-Kunz functions of cubic curves and surfaces

Details Hilbert-Kunz functions of cubic curves and surfaces Hilbert-Kunz functions of cubic curves and surfaces

1996-10-09

arxiv.org/abs/alg-geom/9610009v1

Mathematics

Commutative Algebra

LaTex 2e with Xy-pic v3.2 for commutative diagrams

Scientific paper

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.

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