论文标题
Lagrangian课程在K3表面上的分解
Decomposition of Lagrangian classes on K3 surfaces
论文作者
论文摘要
我们研究了K3表面上拉格朗日同源类别的可分解性，分为由特殊Lagrangian Submanifolds代表的一类总和，并根据晶格理论为其制定标准。结果，我们证明了与Kähler锥体密集子集中的Kähler类别在任意K3表面上的可分解性。使用相同的技术，我们表明在K3表面上的Kähler类也允许特殊的Lagrangian纤维化形成一个密集的子集。这意味着在任何log calabi-yau 3倍的log calabi-yau中都有许多特殊的Lagrangian 3-tori。
We study the decomposability of a Lagrangian homology class on a K3 surface into a sum of classes represented by special Lagrangian submanifolds, and develop criteria for it in terms of lattice theory. As a result, we prove the decomposability on an arbitrary K3 surface with respect to the Kähler classes in dense subsets of the Kähler cone. Using the same technique, we show that the Kähler classes on a K3 surface which admit a special Lagrangian fibration form a dense subset also. This implies that there are infinitely many special Lagrangian 3-tori in any log Calabi-Yau 3-fold.
