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Sulla seminormalità delle superficie algebriche. (Italian) Zbl 0446.14015

In this paper the author proves that a surface \(S\) in \(\mathbb P^4\) is seminormal if and only if its singular points are of the following three types: (1) isolated normal points; (2) isolated double points with tangent cone composed of two planes intersecting in one point; (3) curves \(C\) of points of multiplicity 2 or 3 (generically) and of “general type” (roughly, at the generic point of \(C\) the tangent cone is composed of 2, resp. 3, planes with a line in common and otherwise independent).
This result proves also that a generic projection in \(\mathbb P^4\) of a non-singular surface (of characteristic 0) is seminormal.

MSC:

14J17 Singularities of surfaces or higher-dimensional varieties
14J25 Special surfaces
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References:

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