Grothendieck-Lefschetz Theory, Set-Theoretic Complete Intersections and Rational Normal Scrolls

Lucian Badescu, Giuseppe Valla

Using the Grothendieck-Lefschetz theory (see \cite{[SGA2]}) we prove a criterion to deduce that certain subvarieties of ${\mathbb{P}}^n$ of dimension $\ge 2$ are not set-theoretic co…