June 2023 INITIAL DEGREE OF SYMBOLIC POWERS OF IDEALS OF FERMAT CONFIGURATIONS OF POINTS
Thái Thành Nguyễn
Rocky Mountain J. Math. 53(3): 859-874 (June 2023). DOI: 10.1216/rmj.2023.53.859

Abstract

Let n2 be an integer and consider the defining ideal of the Fermat configuration of points in 2: In=(x(ynzn),y(znxn),z(xnyn))R=[x,y,z]. We explicitly compute the least degree of generators (the initial degree) of its symbolic powers in all unknown cases. As direct applications, we verify Chudnovsky’s conjecture, Demailly’s conjecture and the Harbourne–Huneke containment problem, as well as calculate the Waldschmidt constant and (asymptotic) resurgence number.

Citation

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Thái Thành Nguyễn. "INITIAL DEGREE OF SYMBOLIC POWERS OF IDEALS OF FERMAT CONFIGURATIONS OF POINTS." Rocky Mountain J. Math. 53 (3) 859 - 874, June 2023. https://doi.org/10.1216/rmj.2023.53.859

Information

Received: 10 January 2022; Revised: 19 July 2022; Accepted: 21 July 2022; Published: June 2023
First available in Project Euclid: 21 July 2023

MathSciNet: MR4617916
Digital Object Identifier: 10.1216/rmj.2023.53.859

Subjects:
Primary: 13F20 , 14N20
Secondary: 14C20

Keywords: containment problem , Fermat ideals , Fermat points configuration , ideals of points , Interpolation problem , resurgence number , stable Harbourne–Huneke conjecture , symbolic powers , Waldschmidt constant

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 3 • June 2023
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