@article{CARVAJALROJAS202025,
title = {The uniform symbolic topology property for diagonally F-regular algebras},
journal = {Journal of Algebra},
volume = {548},
pages = {25-52},
year = {2020},
issn = {0021-8693},
doi = {https://doi.org/10.1016/j.jalgebra.2019.11.017},
url = {https://www.sciencedirect.com/science/article/pii/S0021869319306465},
author = {Javier Carvajal-Rojas and Daniel Smolkin},
keywords = {Symbolic powers, Frobenius, Ideal topologies, Singularities, Cartier algebras, Test ideals},
abstract = {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 k-algebras. We also show that this class contains certain singular algebras, such as the affine cone over Pkr×Pks, when k is perfect. By reduction to positive characteristic, it follows that USTP holds effectively for the affine cone over PCr×PCs and more generally for complex varieties of diagonal F-regular type.}
}