The Hilbert-Kunz Function for Binomial Hypersurfaces | Zendy

Shyamashree Upadhyay | Zendy

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The Hilbert-Kunz Function for Binomial Hypersurfaces

Author(s) -

Shyamashree Upadhyay

Publication year - 2014

Publication title -

algebra

Language(s) - English

Resource type - Journals

eISSN - 2314-4114

pISSN - 2314-4106

DOI - 10.1155/2014/525467

Subject(s) - hypersurface , mathematics , multiplicity (mathematics) , binomial (polynomial) , pure mathematics , integer (computer science) , function (biology) , mathematical analysis , statistics , computer science , evolutionary biology , biology , programming language

I give an iterative closed form formula for the Hilbert-Kunz function for any binomial hypersurface in general, over any field of arbitrary positive characteristic. I prove that the Hilbert-Kunz multiplicity associated with 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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