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F-Rationality of Rees Algebras

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

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 262 KB
Volume: 247
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8998

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✦ Synopsis

In this paper, using the notion of the tight integral closure, we will give a criterion for F-rationality of Rees algebras of ᒊ-primary ideals in a Ž . 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 Ž . 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-Ž . Ž . rational. 2 If both A and R I are F-rational, then so is the extended Rees

On the other hand, using resolution of singularities, we will prove that a two-dimensional rational singularity always admits F-rational Rees algebras. In Ž particular, this theorem gives another way than that devised by Watanabe 1997, J.

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