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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Complete ideals and monoidal transforms


Author: Arthur Mattuck
Journal: Proc. Amer. Math. Soc. 26 (1970), 555-560
MSC: Primary 14.18
DOI: https://doi.org/10.1090/S0002-9939-1970-0265362-8
MathSciNet review: 0265362
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Abstract: It is proved that the monoidal transform of an integral noetherian scheme with respect to a sheaf $ I$ of ideals is normal if and only if high powers of $ I$ are complete. The analogous theorem for linear systems is included, and as an application, it is proved that a rational singularity is absolutely isolated.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0265362-8
Keywords: Monoidal transform, quadratic transform, complete ideal, rational singularity, normal variety
Article copyright: © Copyright 1970 American Mathematical Society