Hilbert-Kunz functions of cubic curves and surfaces

Qun Chen; Ragnar-Olaf Buchweitz

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arxiv alg-geom/9610009 v1 pith:TXJVHKWU submitted 1996-10-09 alg-geom math.ACmath.AG

Hilbert-Kunz functions of cubic curves and surfaces

Ragnar-Olaf Buchweitz , Qun Chen This is my paper

classification alg-geom math.ACmath.AG

keywords hilbert-kunzcurvescubicfunctionscharacteristicfunctiongeneralizedplane

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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.

Hilbert-Kunz functions of cubic curves and surfaces

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