论文标题
球形曲折，关系和K3表面的自动等量组的中心
Spherical twists, relations and the center of autoequivalence groups of K3 surfaces
论文作者
论文摘要
同源镜对称性预测，在calabi-yau品种上的相干滑轮类别的自动等效性组与符号歧管的符号映射类组之间存在关系。在本文中，作为Dehn曲折的类似物，我们研究了针对DG增强的三角形类别的球形曲折。 我们介绍了相交数，并将其与球形曲折的群体理论特性相关联。在绘制班级组的理论中，我们表现出类似于基本不平等的不平等，该理论是通过dehn twists的迭代来绘制交叉路口数量的行为的。我们还使用相交编号对两个球形曲折产生的亚组进行了分类。顺便说一句，我们证明了在分级双数上的有限尺寸DG模块的结构定理，并使用它来描述自动等效性组。 作为应用程序，我们计算了K3表面类别的自动等量组的中心。
Homological mirror symmetry predicts that there is a relation between autoequivalence groups of derived categories of coherent sheaves on Calabi-Yau varieties, and the symplectic mapping class groups of symplectic manifolds. In this paper, as an analogue of Dehn twists for closed oriented real surfaces, we study spherical twists for dg-enhanced triangulated categories. We introduce the intersection number and relate it to group-theoretic properties of spherical twists. We show an inequality analogous to a fundamental inequality in the theory of mapping class groups about the behavior of the intersection number via iterations of Dehn twists. We also classify the subgroups generated by two spherical twists using the intersection number. In passing, we prove a structure theorem for finite dimensional dg-modules over the graded dual numbers and use this to describe the autoequivalence group. As an application, we compute the center of autoequivalence groups of derived categories of K3 surfaces.
