The Hilbert-Kunz Function for Binomial Hypersurfaces. (27th November 2014)

• Record Type: Journal Article
• Authors: Upadhyay, Shyamashree
• Other Names: Sahoo Prasanna Kumar Academic Editor.
• Is Part Of: Algebra. Volume 2014(2014)
• Publication Date: 2014-11-27
• Subjects: Algebra -- Periodicals; Algebra; Electronic journals; Periodicals; 512.005
• DOI: 10.1155/2014/525467
• Languages: English
• ISSNs: 2314-4106

Abstract

Abstract : 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.