  Suppose that $X$ is a smooth complex algebraic variety of dimension $\geq 3$
and $f$ defines a hypersurface $Z$ in $X$, with a unique singular point $P$.
Bitoun and Schedler conjectured that the ${\mathcal D}$-module generated by
$\tfrac{1}{f}$ has length equal to $g_P(Z)+2$, where $g_{P}(Z)$ is the reduced
genus of $Z$ at $P$. We prove that this length is always $\geq g_P(Z)+2$ and
equality holds if and only if $\tfrac{1}{f}$ lies in the ${\mathcal D}$-module
generated by $I_0(f)\tfrac{1}{f}$, where $I_0(f)$ is the multiplier ideal
${\mathcal J}(f^{1-\epsilon})$, with $0<\epsilon\ll 1$. In particular, we see
that the conjecture holds if the pair $(X,Z)$ is log canonical. We can also
recover, with an easy proof, the result of Bitoun and Schedler saying that the
conjecture holds for weighted homogeneous isolated singularities. On the other
hand, we give an example (a polynomial in $3$ variables with an ordinary
singular point of multiplicity $4$) for which the conjecture does not hold.
