F-rationality of Rees algebras

Nobuo Hara, Kei Ichi Watanabe, Ken Ichi Yoshida

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

In this paper, using the notion of the tight integral closure, we will give a criterion for F-rationality of Rees algebras of m-primary ideals in a Cohen-Macaulay local ring. As its application, we prove the following results: (1) In dimension two, if A is F-rational and I is integrally closed, then the Rees algebra R(I) is F-rational. On the other hand, in higher dimensions, we construct many examples of Cohen-Macaulay, normal Rees algebras which are not F-rational. (2) If both A and R(I) are F-rational, then so is the extended Rees algebra R'(I). (3) If R(I) is F-rational and a(G(I)) ≠ - 1, then A is F-rational. On the other hand, using resolution of singularities, we will prove that a two-dimensional rational singularity always admits F-rational Rees algebras. In particular, this theorem gives another way than that devised by Watanabe (1997, J. Pure Appl. Algebra 122, 323-328) to construct counterexamples to the Boutot-type theorem for F-rational rings.

Original languageEnglish
Pages (from-to)153-190
Number of pages38
JournalJournal of Algebra
Volume247
Issue number1
DOIs
Publication statusPublished - 2002 Jan 1

Keywords

  • F-rationality
  • Rational singularity
  • Rees ring
  • Tight integral closure

ASJC Scopus subject areas

  • Algebra and Number Theory

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    Hara, N., Watanabe, K. I., & Yoshida, K. I. (2002). F-rationality of Rees algebras. Journal of Algebra, 247(1), 153-190. https://doi.org/10.1006/jabr.2001.8998