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

2007/01/04 by José Carlos Sierra, Sierra, José Carlos
Mathematics · #14M07 #14N05 (Primary) 14D06 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14D06 #msc:14M07 #msc:14N05

paper · pdf · doi:10.48550/arxiv.math/0701138

19 pages. Final version. To appear in International Journal of Mathematics

arxiv created 2008/06/23 · arxiv updated 2009/12/01

Abstract

A classification and a detailed geometric description are given for smooth n-dimensional subvarieties X⊂\mathbb P^2n-1 containing a family of effective divisors each of them spanning a linear \mathbb Pⁿ of \mathbb P^2n-1. Some results on multisecant lines to threefolds X⊂\mathbb P⁵ follow, as a byproduct.

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