The singular-locus dimension conjecture for foliations of low dimension

Let $X$ be a complex manifold of dimension $n$ and let $\mathscr F$ be a foliation of dimension $k$ with $k\leq n/2$. If the singular locus $\operatorname{Sing}(\mathscr F)$ is non-empty, it contains a component of dimension at least $k-1$.

Low-dimensional foliation singular-locus conjecture. The stated dimension bound should hold for every such foliation.

The source presents this as a generalized version of the Cerveau–Lins Neto problem and proves the assertion in this range, so the conjectural statement is solved in the paper.