Algebraic Barth-Lefschetz theorems

Details Algebraic Barth-Lefschetz theorems Algebraic Barth-Lefschetz theorems

1995-05-08

arxiv.org/abs/alg-geom/9505010v1

Mathematics

Algebraic Geometry

18 pages, to appear in Nagoya Mathematical Journal. AMSTeX v. 2.1

Scientific paper

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 ${\Delta}_Y$ 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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