  Let $X$ be a codimension two nonsingular subvariety of a nonsingular quadric
$\Q{n}$ of dimension $n\geq 5$. We classify such subvarieties when they are
scrolls. We also classify them when the degree $d\leq 10$. Both results were
known when $n=4$.
  Keywords: Classification; liaison; low codimension; low degree; quadric;
scroll; vector bundle

Algebraic Geometry;Algebraic Geometry