Singularity of $\mathbb{Q}$-divisors of multidegree one in multiprojective space

Abstract

We study singularity of effective $\mathbb{Q}$-divisors on products of projective spaces of multidegree $(1,1...,1).$ This generalizes works of Bath, Musta{\c{t}}{\u{a}} and Walther on singularity of square-free polynomials. We also give a lower bound on the log canonical threshold of a hypersurface in products of projective spaces.