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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Hyperplanarity of the equimultiple locus


Author: R. Narasimhan
Journal: Proc. Amer. Math. Soc. 87 (1983), 403-408
MSC: Primary 14B05; Secondary 13H05, 13H15, 14J17
MathSciNet review: 684627
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Abstract: It is known that the (local) equimultiple locus of a hypersurface defined over a field of characteristic zero is contained in a hyperplane (for example, the one given by the Tchirnhausen transformation: see Abhyankar's paper [A] for details). In this note (a) we show that this theorem is no longer true for varieties of dimension bigger than two in char $ p > 0$, and (b) we give proofs of this statement in the cases of

(i) 'purely inseparable' surfaces,

(ii) double points of surfaces in char 2.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0684627-8
PII: S 0002-9939(1983)0684627-8
Keywords: Equimultiplicity, equimultiple locus, hyperplane, Dedekind conductor formula
Article copyright: © Copyright 1983 American Mathematical Society