A counterexample to the parity conjecture

Let $[Z]\in\textnormal{Hilb}^d\mathbb{A}^3$ be a zero-dimensional subscheme of the affine three-dimensional complex space of length $d>0$. Okounkov and Pandharipande have conjectured that the dimension of the tangent space to $\textnormal{Hilb}^d\mathbb{A}^3$ at $[Z]$ and $d$ have have the same parity. The conjecture was proven by Maulik, Nekrasov, Okounkov and Pandharipande for points $[Z]$ defined by monomial ideals and very recently by Ramkumar and Sammartano for homogeneous ideals. In this paper we exhibit a family of zero-dimensional schemes in $\textnormal{Hilb}^{12} \mathbb{A}^3$, which disproves the conjecture in the general non-homogeneous case.