Details:
Title  HilbertKunz functions of $2times 2$ determinantal rings.  Author(s)  Lance Edward Miller, Irena Swanson  Type  Article in Journal  Abstract  Let k be an arbitrary field (of arbitrary characteristic) and let X=[xi,j] be a generic m×n matrix of variables. Denote by I2(X) the ideal in k[X]=k[xi,j:i=1,…,m;j=1,…,n] generated by the 2×2 minors of X. Using Gröbner basis, we give a recursive formulation for the lengths of the k[X]module k[X]/(I2(X)+(xq1,1,…,xqm,n)) as q varies over all positive integers. This is a generalized Hilbert–Kunz function, and our formulation proves that it is a polynomial function in q. We apply our method to give closed forms for these Hilbert–Kunz functions for cases m≤2.  ISSN  00192082 
URL 
http://projecteuclid.org/euclid.ijm/1403534495 
Language  English  Journal  Ill. J. Math.  Volume  57  Number  1  Pages  251277  Publisher  University of Illinois, Department of Mathematics, Urbana, IL  Year  2013  Edition  0  Translation 
No  Refereed 
No 
