Hyperplanarity of the equimultiple locus
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- by R. Narasimhan PDF
- Proc. Amer. Math. Soc. 87 (1983), 403-408 Request permission
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.References
- Shreeram S. Abhyankar, Good points of a hypersurface, Adv. in Math. 68 (1988), no. 2, 87–256. MR 934366, DOI 10.1016/0001-8708(88)90015-1
- Masayoshi Nagata, Local rings, Robert E. Krieger Publishing Co., Huntington, N.Y., 1975. Corrected reprint. MR 0460307
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 403-408
- MSC: Primary 14B05; Secondary 13H05, 13H15, 14J17
- DOI: https://doi.org/10.1090/S0002-9939-1983-0684627-8
- MathSciNet review: 684627