Rees algebras of F-regular type

Nobuo Hara, Kei Ichi Watanabe, Ken Ichi Yoshida

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We study the F-regularity of Rees algebras R(I) = A[It] in terms of the global F-regularity of the blowing-up X = Proj R(I) of Spec A. As it reads, global F-regularity is a global analog of strong F-regularity defined via splitting of Frobenius maps in prime characteristic, and these notions are extended to characteristic zero by reduction modulo p ≫ 0. We study in detail the case where (A, m) is a two-dimensional local ring and I is an m-primary ideal. In characteristic zero, the condition for R(I) to have F-regular type is described in terms of the dual graph of a resolution X on which IOX is invertible. We also prove some miscellaneous results concerning singularities of Rees algebras and extended Rees algebras of higher dimension.

Original languageEnglish
Pages (from-to)191-218
Number of pages28
JournalJournal of Algebra
Volume247
Issue number1
DOIs
Publication statusPublished - 2002 Jan 1

Keywords

  • (Strongly) F-regular
  • Globally f-regular
  • Modulo p reduction
  • Rees algebra
  • Singularity

ASJC Scopus subject areas

  • Algebra and Number Theory

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    Hara, N., Watanabe, K. I., & Yoshida, K. I. (2002). Rees algebras of F-regular type. Journal of Algebra, 247(1), 191-218. https://doi.org/10.1006/jabr.2001.9000