Smooth $n$-dimensional subvarieties of ${\mathbb{P}}^{2n-1}$ containing a family of very degenerate divisors

Abstract

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.

arXiv comment19 pages. Final version. To appear in International Journal of Mathematics

References in corpus (1)

• Conic bundles in projective fourspace