The converse higher Du Bois–rational singularities conjecture

Let $X$ be a variety with lci singularities, and let $k$-Du Bois and $(k-1)$-rational denote the higher Du Bois and higher rational singularity conditions.

Higher Du Bois implies lower rational conjecture. If $X$ has lci singularities and $X$ is $k$-Du Bois, then $X$ is $(k-1)$-rational.

This conjecture was made in the first version of the paper and reflects the close relationship between higher rational and higher Du Bois singularities, particularly for isolated complete intersections. The supplied text gives no resolution status.