F-Rationality of Determinantal Rings and Their Rees Rings

摘要

Let X be an m × n matrix (m ≤ n) of indeterminates over a field K of positive characteristic, and denote the ideal generated by its t-minors by I_t. We show that the Rees ring R(I_t) of K[X], as well as the algebra A_t generated by the t-minors, are F-rational if char K ＞ min (t, m-t). Without a restriction on characteristic this holds for K[X].I_r+1 and the symbolic Rees ring R~s(I_t). The determinantal ring K[X]/I_r+1 is actually F-regular, as was previously proved by Hochster and Huneke [13] and Conca and Herzog [5] through different approaches.