Smooth $n$-dimensional subvarieties of ${\mathbb P}^{2n-1}$ containing a family of very degenerate divisors
Abstract
Description
A classification and a detailed geometric description are given for smooth $n$-dimensional subvarieties $X\subset{\mathbb P}^{2n-1}$ containing a family of effective divisors each of them spanning a linear ${\mathbb P}^n$ of ${\mathbb P}^{2n-1}$. Some results on multisecant lines to threefolds $X\subset{\mathbb P}^5$ follow, as a byproduct.
19 pages. Final version. To appear in International Journal of Mathematics
19 pages. Final version. To appear in International Journal of Mathematics