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Algebraic Barth-Lefschetz theorems

Lucian Badescu
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Abstract

Using results of Hironaka-Matsumura and Faltings, we prove a strong version of the well known Fulton-Hansen connectivity theorem for weighted projective spaces. As a consequence we get the following result. If $Y$ is an irreducible subvariety of the $n$-dimensional projective space (over a field of arbitrary characteristic), then the diagonal embedding $Δ_Y$ is $G_3$ in $Y\times Y$. This fact implies a generalized version (with a characteristic-free proof) of a result of Ogus (in char. zero) and Speiser (in positive characteristic).

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Lucian Badescu. 1995-05-08. Algebraic Barth-Lefschetz theorems. https://arxiv.org/abs/alg-geom/9505010

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