The uniform symbolic topology property for diagonally F-regular algebras

Let k be a field of positive characteristic. Building on the work of the second named author, we define a new class of k-algebras, called diagonally F-regular algebras, for which the so-called Uniform. Symbolic Topology Property (USTP) holds effectively. We show that this class contains all essentially smooth if-algebras. We also show that this class contains certain singular algebras, such as the affine cone over P-k(r) x P-k(s) when k is perfect. By reduction to positive characteristic, it follows that USTP holds effectively for the affine cone over P-C(r) x P-C(s) and more generally for complex varieties of diagonal F-regular type. (C) 2019 Elsevier Inc. All rights reserved.