On the Frobenius complexity of determinantal rings

Abstract

We compute the Frobenius complexity for the determinantal ring of prime characteristic $p$ obtained by modding out the $2\times 2$ minors of an $m\times n$ matrix of indeterminates, where $m>n\ge 2$. We also show that, as $p\to \infty$, the Frobenius complexity approaches $m-1$.

18 pages, comments welcome; new material added regarding the limit of Frobenius complexity as p goes to infinity and connections to the Perron-Frobenius theorem. arXiv admin note: text overlap with arXiv:1401.0234