We show that Hilbert schemes of points on supersingular Enriques surface in characteristic 2, $Hil{b}^n(X)$, for $n\ge 2$ are simply connected, symplectic varieties but are not irreducible symplectic as the hodge number $h^{2,0}>1$, even though a supersingular Enriques surface is an irreducible symplectic variety. These are the classes of varieties which appear only in characteristic 2 and they show that the hodge number formula for Göttsche-Soergel does not hold over characteristic 2. It also gives examples of varieties with trivial canonical class which are neither irreducible symplectic nor Calabi-Yau, thereby showing that there are strictly more classes of simply connected varieties with trivial canonical class in characteristic 2 than over $\mathbb{C}$ as given by Beauville-Bogolomov decomposition theorem.

我们证明了特征2中超奇异Enriques曲面上的点的希尔伯特方案 $H\mathrm{一世}升b^{ñ}（X）$， 为了 $ñ\ge 2$ 是简单相连的辛型，但不是不可约的辛奇数 $H^{2，0}>\mathrm{1个}$，即使超奇的Enriques曲面是一个不可约的辛形。这些是仅出现在特征2中的类别，它们表明Göttsche-Soergel的霍奇数公式不超过特征2。它还给出了具有普通典范类别且既不可简化的辛也不是Calabi-Yau的品种的示例，因此表明在特征2中，具有平凡规范类的简单连通品种的类严格大于$\mathbb{C}$ 由Beauville-Bogolomov分解定理给出。