The uniform symbolic topology property for diagonally F-regular algebras

JOURNAL OF ALGEBRA

卷:548

Article

Carvajal-Rojas, Javier^1,2  Smolkin, Daniel³ 

[1] Ecole Polytech Fed Lausanne, SB MATH CAG, MA C3 615,Batiment MA,Stn 8, CH-1015 Lausanne, Switzerland

[2] Univ Costa Rica, Escuela Matemat, San Jose 11501, Costa Rica

[3] Univ Oklahoma, Dept Math, 601 Elm Ave,Room 423, Norman, OK 73019 USA

关键词: Symbolic powers;    Frobenius;    Ideal topologies;    Singularities;    Cartier algebras;    Test ideals;   

DOI  :  10.1016/j.jalgebra.2019.11.017

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free