Let V/k be an irreducible algebraic variety of dimension ≥3, defined over a field k of characteristic O, passing through the origin (O) of the ambient affine n-space. Let p be the prime ideal of V in the polynomial ring k[X1, ..., Xn]. If V/k is k-normal at (O), then for almost all hyperplanes Ha: a1X1+...+anXn=0 with a1, ..., an ε k the ideal (p, a1X1+...+anXn) is a prime ideal. If the generic hyperplane section of V through (O) is normal over the ground field of the generic section of V, then the section V ∩ Ha is k-normal at (O) for almost all Ha.
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Entrata in Redazione il 1 ottobre 1971.
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Kuan, W. Specialization of a generic hyperplane section through a rational point of an algebraic variety. Annali di Matematica 94, 75–82 (1972). https://doi.org/10.1007/BF02413603
- Prime Ideal
- Rational Point
- Algebraic Variety
- Polynomial Ring
- Section Versus