Noether-Lefschetz Theory and Néron-Severi Group

Vincenzo Di Gennaro, Davide Franco

Published 2009-04-29Version 1

Let $Z$ be a closed subscheme of a smooth complex projective complete intersection variety $Y\subseteq \Ps^N$, with $dim Y=2r+1\geq 3$. We describe the N\'eron-Severi group $NS_r(X)$ of a general smooth hypersurface $X\subset Y$ of sufficiently large degree containing $Z$.