论文标题
圆锥体的圆锥体量表calabi-yau表面
A cone conjecture for log Calabi-Yau surfaces
论文作者
论文摘要
我们认为log log calabi-yau表面$（y，d）$具有单数边界。在每种变形类型中，都有一个杰出的表面$（y_e，d_e）$，使得$ h_2（y \ setminus d）$上的混合霍奇结构被拆分。我们证明（1）$（y_e，d_e）$在其nef有效锥体上的自动形态组的行动承认一个理性的多面体基本域； （2）单模组对变形类型中非常通用表面的NEF有效锥的作用，接受了一个理性的多面体基本结构域。这些陈述可以看作是log calabi-yau表面的Morrison锥体的版本。此外，如果$ d $的组件数量为$ \ le 6 $，我们表明$ y_e $的nef锥体是理性的多面体，并明确描述它。这提供了无限的莫里梦境新例子。
We consider log Calabi-Yau surfaces $(Y, D)$ with singular boundary. In each deformation type, there is a distinguished surface $(Y_e,D_e)$ such that the mixed Hodge structure on $H_2(Y \setminus D)$ is split. We prove that (1) the action of the automorphism group of $(Y_e,D_e)$ on its nef effective cone admits a rational polyhedral fundamental domain; and (2) the action of the monodromy group on the nef effective cone of a very general surface in the deformation type admits a rational polyhedral fundamental domain. These statements can be viewed as versions of the Morrison cone conjecture for log Calabi--Yau surfaces. In addition, if the number of components of $D$ is $\le 6$, we show that the nef cone of $Y_e$ is rational polyhedral and describe it explicitly. This provides infinite series of new examples of Mori Dream Spaces.
