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Rees Algebras of F-regular Type

✍ Scribed by Nobuo Hara; Kei-ichi Watanabe; Ken-ichi Yoshida

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 195 KB
Volume: 247
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.9000

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✦ Synopsis

We study the F-regularity of Rees algebras R I s A It in terms of the global Ž . F-regularity of the blowing-up X s 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 charac-Ž . teristic zero by reduction modulo p 4 0. We study in detail the case where A, ᒊ is a two-dimensional local ring and I is an ᒊ-primary ideal. In characteristic zero, Ž . the condition for R I to have F-regular type is described in terms of the dual graph of a resolution X on which IO O is invertible. We also prove some X miscellaneous results concerning singularities of Rees algebras and extended Rees algebras of higher dimension.

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