2023/05/21 by Nirmal Kotal, Kotal, Nirmal, Manoj Kummini +1
Mathematics · #13A30 #13A35 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2305.12383
openalex publication_date 2023/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove some sufficient conditions for Cohen-Macaulay normal Rees algebras to be F-rational. Let (R,\mathfrakm) be a Gorenstein normal local domain of dimension d≥ 2 and of characteristic p > 0. Let I be a \mathfrakm-primary ideal. Our first set of results give conditions on the test ideals τ(In), n ≥ 1 which would imply that the normalization of the Rees algebra R[It] is F-rational. Another sufficient condition is that the socle of H_G+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[\mathfrakm t ]) is F-rational, then R[\mathfrakm t ] is F-rational.