Codimension bounds for the Noether-Lefschetz components for toric varieties

Ugo Bruzzo, William D. Montoya

For a quasi-smooth hyper-surface $X$ in a projective simplicial toric variety $P$, the morphism $i:H^p(P)\to H^p(X)$ induced by the inclusion is injective for $p=d$ and an isomorp…