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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
- Michael Artin, On isolated rational singularities of surfaces, Amer. J. Math. 88 (1966), 129–136. MR 199191, DOI https://doi.org/10.2307/2373050
- Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960. MR 0120249
- D. Rees, Valuations associated with ideals, Proc. London Math. Soc. (3) 6 (1956), 161–174. MR 77513, DOI https://doi.org/10.1112/plms/s3-6.2.161 A. Grothendieck, Éléments de géométrie algébrique, Inst. Hautes Études Sci. Publ. Math. No. 11 (1961). MR 36 #177.
- Serge Lang, Introduction to algebraic geometry, Interscience Publishers, Inc., New York-London, 1958. MR 0100591
- Egbert Brieskorn, Rationale Singularitäten komplexer Flächen, Invent. Math. 4 (1967/68), 336–358 (German). MR 222084, DOI https://doi.org/10.1007/BF01425318
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14.18
Retrieve articles in all journals with MSC: 14.18
Additional Information
Keywords:
Monoidal transform,
quadratic transform,
complete ideal,
rational singularity,
normal variety
Article copyright:
© Copyright 1970
American Mathematical Society