Home | Quick Search | Advanced Search | Bibliography submission | Bibliography submission using bibtex | Bibliography submission using bibtex file | Links | Help | Internal

Details:

   
TitleHilbert-Kunz functions of $2times 2$ determinantal rings.
Author(s) Lance Edward Miller, Irena Swanson
TypeArticle in Journal
AbstractLet 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.
ISSN0019-2082
URL http://projecteuclid.org/euclid.ijm/1403534495
LanguageEnglish
JournalIll. J. Math.
Volume57
Number1
Pages251--277
PublisherUniversity of Illinois, Department of Mathematics, Urbana, IL
Year2013
Edition0
Translation No
Refereed No
Webmaster