# Explicit Hilbert–Kunz functions of 2 × 2 determinantal rings

@article{Miller2015ExplicitHF,
title={Explicit Hilbert–Kunz functions of 2 × 2 determinantal rings},
author={L. Miller and I. Swanson},
journal={Pacific Journal of Mathematics},
year={2015},
volume={275},
pages={433-442}
}
• Published 2015
• Mathematics
• Pacific Journal of Mathematics
• Let $k[X] = k[x_{i,j}: i = 1,..., m; j = 1,..., n]$ be the polynomial ring in $m n$ variables $x_{i,j}$ over a field $k$ of arbitrary characteristic. Denote by $I_2(X)$ the ideal generated by the $2 \times 2$ minors of the generic $m \times n$ matrix $[x_{i,j}]$. We give a closed formulation for the dimensions of the $k$-vector space $k[X]/(I_2(X) + (x_{1,1}^q,..., x_{m,n}^q))$ as $q$ varies over all positive integers, i.e., we give a closed form for the generalized Hilbert-Kunz function of the… CONTINUE READING
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