Table of Contents
Algebra
Volume 2014, Article ID 525467, 15 pages
http://dx.doi.org/10.1155/2014/525467
Research Article

The Hilbert-Kunz Function for Binomial Hypersurfaces

Department of Mathematics, Indian Institute of Technology, Guwahati, Assam 781039, India

Received 6 August 2014; Revised 18 October 2014; Accepted 21 October 2014; Published 27 November 2014

Academic Editor: Prasanna Kumar Sahoo

Copyright © 2014 Shyamashree Upadhyay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.