Winter 2024 BLOW-UP RINGS AND F-RATIONALITY
Nirmal Kotal, Manoj Kummini
J. Commut. Algebra 16(4): 439-457 (Winter 2024). DOI: 10.1216/jca.2024.16.439

Abstract

In this paper, we prove some sufficient conditions for Cohen–Macaulay normal Rees algebras to be F-rational. Let (R,𝔪) be a Gorenstein normal local domain of dimension d2 and of characteristic p>0. Let I be an ideal generated by a system of parameters. Our first set of results give conditions on the test ideals τ(In), n1 which would imply that the normalization of the Rees algebra R[It] is F-rational. Another sufficient condition is that the socle of HG¯+d(G¯) (where G¯ is the associated graded ring for the integral closure filtration) is entirely in degree 1, if R is F-rational (but not necessarily Gorenstein). Then we show that if R is a hypersurface of degree 2 or is three-dimensional and F-rational and Proj(R[𝔪t]) is F-rational, then R[𝔪t] is F-rational.

Citation

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Nirmal Kotal. Manoj Kummini. "BLOW-UP RINGS AND F-RATIONALITY." J. Commut. Algebra 16 (4) 439 - 457, Winter 2024. https://doi.org/10.1216/jca.2024.16.439

Information

Received: 18 October 2023; Revised: 7 March 2024; Accepted: 12 March 2024; Published: Winter 2024
First available in Project Euclid: 6 January 2025

Digital Object Identifier: 10.1216/jca.2024.16.439

Subjects:
Primary: 13A30 , 13A35

Keywords: F-rationality , Rees algebras , test ideals

Rights: Copyright © 2024 Rocky Mountain Mathematics Consortium

Vol.16 • No. 4 • Winter 2024
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