2 problems

Log weak Lefschetz conjecture. Assume that $\mathcal O_Y(E)$ is ample. Then the morphism above is a filtered isomorphism with respect to $P$ if $q\leq d-2$ and strictly injective f…

Weak Lefschetz conjecture. This map is an isomorphism when $2p<\dim(L)$ and is injective modulo torsion when $2p=\dim(L)$. This is the Chow-group analogue of the classical Weak Lef…