2018/07/11 by Javier Carvajal-Rojas, Javier Carvajal‐Rojas, Daniel Smolkin · 5 citations
Mathematics · #Affine transformation #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Algorithm #Class (philosophy) #Combinatorics #Computer science #Cone (formal languages) #Diagonal #Discrete mathematics #Field (mathematics) #Geometry #Mathematics #Pure mathematics #Reduction (mathematics) #Rings, Modules, and Algebras #Topology (electrical circuits) #Type (biology) #math.AC #math.AG #msc:13A15 #msc:13A35 #msc:13C99 #msc:14B05
paper · pdf · doi:10.1016/j.jalgebra.2019.11.017
published in Journal of Algebra 548, 25-52 (Elsevier BV) · 22 pages. Comments welcome
arxiv created 2018/07/11 · openalex publication_date 2019/12/02 · arxiv updated 2022/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 ℙrk × ℙsk, when k is perfect. By reduction to positive characteristic, it follows that USTP holds effectively for the affine cone over ℙrℂ × ℙsℂ and more generally for complex varieties of diagonal F-regular type.