Algebraic Barth-Lefschetz theorems
Abstract
Description
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).
18 pages, to appear in Nagoya Mathematical Journal. AMSTeX v. 2.1
18 pages, to appear in Nagoya Mathematical Journal. AMSTeX v. 2.1