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Gherardelli linkage and complete intersections

Davide Franco·Steven L. Kleiman·Alexandru T. Lascu
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Abstract

Our main theorem characterizes the complete intersections of codimension 2 in a projective space of dimension 3 or more over an algebraically closed field of characteristic 0 as the subcanonical and self-linked subschemes. In order to prove this theorem, we'll prove the Gherardelli linkage theorem, which asserts that a partial intersection of two hypersurfaces is subcanonical if and only if its residual intersection is, scheme-theoretically, the intersection of the two hypersurfaces with a third.

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Davide Franco, Steven L. Kleiman, Alexandru T. Lascu. 2000-03-13. Gherardelli linkage and complete intersections. https://arxiv.org/abs/math/0003075

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