1. On Rational Varieties Smooth Except at a Seminormal Singular Point.
- Author
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Cioffi, Francesca, Orecchia, Ferruccio, and Ramella, Luciana
- Subjects
MATHEMATICAL singularities ,CHARACTERISTIC functions ,PROJECTIVE spaces ,MATHEMATICS ,MATHEMATICAL analysis ,ALGEBRA ,ALGEBRAIC geometry - Abstract
We construct a class of projective rational varieties X of any dimension m ≥ 1, which are smooth except at a point O, with the projective space ℙ m as normalization, having smooth branches, and reduced projectivized tangent cone in O. The Hilbert function of X is considered and is explicitly computed when the point O is seminormal. Indeed, we study seminormality, obtaining necessary and sufficient conditions for O to be seminormal and show that in such case the tangent cone is reduced and seminormal. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
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