The Hilbert-Kunz function for Binomial Hypersurfaces

Details The Hilbert-Kunz function for Binomial Hypersurfaces The Hilbert-Kunz function for Binomial Hypersurfaces

2011-01-31

arxiv.org/abs/1101.5936v1

Mathematics

Combinatorics

19 pages

Scientific paper

In this article, I give an iterative closed form formula for the Hilbert-Kunz function for any binomial hypersurface in general, over any feild of arbitrary positive characteristic. I prove that the Hilbert-Kunz multiplicity associated to any Binomial Hypersurface over any field of arbitrary positive characteristic is rational. As an example, I also prove the well known fact that for $1$-dimensional Binomial Hypersurfaces, the Hilbert-Kunz multiplicity is a positive integer and give a precise account of the integer.

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