2024/08/10 by Tony J. Puthenpurakal, Puthenpurakal, Tony J.
Mathematics · #13B22 #13H10 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 13A30 #Rings, Modules, and Algebras #Secondary 13D40
paper · pdf · doi:10.48550/arxiv.2408.05532
openalex publication_date 2024/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (A,\mathfrakm) be an excellent normal local ring of dimension d ≥ 2 with infinite residue field. Let I be an \mathfrakm-primary ideal. Then the following assertions are equivalent: (i) The extended Rees algebra A[It, t-1] is R1. (ii) The Rees algebra A[It] is R1. (iii) Proj(A[It]) is R1. (iv) (In)^* = (In)1 for all n ≥ 1. Here (In)^* is the integral closure of In and (In)1 is the first coefficient ideal of In.