A Higher dimensional log Riemann--Hurwitz inequality and rigidity of covers

Donu Arapura, Chikako Mese, Deepam Patel

Let $\overline{Z}$ be a smooth projective variety with an simple normal crossing divisor $D$ such that ${\Omega }_{\overline{Z}}^1(\log D)$ is nef. We prove that if $Y\subset Z:=\overline…