On finite covers of projective spaces, generic outside of codimension three

Source abstract

In the article, we generalize to an arbitrary dimension results obtained by the author and S.Yu. Nemirovski that related to Chisini's conjecture claimed that if $B$ is the discriminant of two generic covers $f_i:X_i\to \mathbb P^2$, $i=1,2$, and $\max (°f_1,°f_2) \geq 5$, then $f_1$ and $f_2$ are equivalent covers.