# IJPAM: Volume 16, No. 1 (2004)

GENERALIZED SECANT VARIETIES AND
JOINS OF PROJECTIVE CURVES

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it

Abstract.Let be an integral non-degenerate variety. For any integer let denote the closure in of the union of all -dimensional linear spaces spanned by a length zero-dimensional subscheme of . may be reducible. Here we show that when and the scheme is irreducible if and only if the curve has only planar singularities. We extend the definition and the result to joins of different varieties.