On the regularity of varieties having an extremal secant line
arXiv:math/0007074
Abstract
The Castelnuovo-Mumford regularity of varieties of degree r and dimension n in the r-dimensional projective space that have an extremal secant line, is at least d-r+n+1. We classify these varieties and show that their regularity is exactly d-r+n+1, as predicted by the regularity conjecture.
12 pages, part of it contains results from my Ph.D. thesis (Columbia University NY)