IJPAM: Volume 18, No. 3 (2005)

SECANT SPACES TO PROJECTIVE
VARIETIES AND THEIR LIMITS, II

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

Abstract.Here we study the case $x = n-\dim (X)+1$ of the following question. For any finite $S \subset {\bf {P}}^n$ let $\langle S \rangle$ denote its linear span. Let $X \subsetneq {\bf {P}}^n$ , $n \ge 2$ , be an integral non-degenerate subvariety. For which pairs such that $Q\in {\bf {P}}^n$ and $x\in \mathbb {Z}$ , $x\ge 2$ , is there $S \subset X$ such that $\sharp (S) = x$ and $Q\in \langle S \rangle$ , but $Q\notin \langle S'\rangle$ for every $S'\subsetneqq S$ ?