A generalization of tight closure and multiplier ideals
Authors:
Nobuo Hara and Ken-ichi Yoshida
Journal:
Trans. Amer. Math. Soc. 355 (2003), 3143-3174
MSC (2000):
Primary 13A35, 14B05
DOI:
https://doi.org/10.1090/S0002-9947-03-03285-9
Published electronically:
April 11, 2003
MathSciNet review:
1974679
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We introduce a new variant of tight closure associated to any fixed ideal , which we call
-tight closure, and study various properties thereof. In our theory, the annihilator ideal
of all
-tight closure relations, which is a generalization of the test ideal in the usual tight closure theory, plays a particularly important role. We prove the correspondence of the ideal
and the multiplier ideal associated to
(or, the adjoint of
in Lipman's sense) in normal
-Gorenstein rings reduced from characteristic zero to characteristic
. Also, in fixed prime characteristic, we establish some properties of
similar to those of multiplier ideals (e.g., a Briançon-Skoda-type theorem, subadditivity, etc.) with considerably simple proofs, and study the relationship between the ideal
and the F-rationality of Rees algebras.
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Additional Information
Nobuo Hara
Affiliation:
Mathematical Institute, Tohoku University, Sendai 980–8578, Japan
Email:
hara@math.tohoku.ac.jp
Ken-ichi Yoshida
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464–8602, Japan
Email:
yoshida@math.nagoya-u.ac.jp
DOI:
https://doi.org/10.1090/S0002-9947-03-03285-9
Received by editor(s):
August 20, 2002
Received by editor(s) in revised form:
December 19, 2002
Published electronically:
April 11, 2003
Additional Notes:
Both authors are partially supported by a Grant-in-Aid for Scientific Research, Japan
Article copyright:
© Copyright 2003
American Mathematical Society