Ramification Divisors of General Projections

Abstract

We study ramification divisors of projections of a smooth projective variety onto a linear space of the same dimension. We prove that for a large class of varieties, the ramification divisors of such projections vary in a maximal dimensional family. We study the map that associates to a linear projection its ramification divisor. By a degeneration argument involving (linked) limit linear series of higher rank, we show that this map is dominant for most (but not all!) varieties of minimal degree.