Hilbert-Kunz functions of cubic curves and surfaces

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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.
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Algebraic Geometry, Commutative Algebra, 11C20, 13H15, 14H45

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http://salesiana.dossiersoluciones.com/handle/123456789/150217

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/alg-geom/9610009
 http://arxiv.org/abs/alg-geom/9610009

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arXiv