Singularities of generic linkage via Frobenius powers

Abstract

Let I I be an equidimensional ideal of a ring polynomial R R over C \mathbb {C} and let J J be its generic linkage. We prove that there is a uniform bound of the difference between the F-pure thresholds of I p I_p and J p J_p via the generalized Frobenius powers of ideals. This provides evidence that the F-pure threshold of an equidimensional ideal I I is less than that of its generic linkage. As a corollary we recover a result on log canonical thresholds of generic linkage by Niu.