论文标题
Hilbert supersingular Enriques表面的Hilbert方案的病理
Pathologies of Hilbert scheme of points of supersingular Enriques surface
论文作者
论文摘要
我们表明，在特征2中，在超明含量的表面上的Hilbert方案简单地连接，象征性品种，但并非不可约合，因为Hodge Number $ H^{2,0}> 1 $，即使Supersingular Enriques表面表面是一种不可估的象征性象征性品种。这些是仅在特征2中出现的品种类别，它们表明，戈特奇 - 塞啤酒的hodge数字公式不存在于特征2。它也给出了具有琐碎的象征性的象征性和calabi-yau的典型范围的典型类别的示例。 $ \ mathbb {c} $由Beauville-Bogolomov分解定理给出。
We show that Hilbert schemes of points on supersingular Enriques surface in characteristic 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.
