论文标题
II型退化K3表面，模量压实和HyperKahler指标的PL密度不变
PL density invariant for type II degenerating K3 surfaces, Moduli compactification and hyperKahler metrics
论文作者
论文摘要
这里的主角是K3表面II型变性的新型不变性，它是从间隔中显式PL（分段线性）凸功能，最多为18个非线性点。忘记其实际功能行为，还将II型退化分为几种组合类型，具体取决于经典示例中出现的根晶格的类型。 从微分几何观点来看，该函数作为折叠式超卡勒指标的限制度量的密度函数，如本田 - 苏恩Zhang的工作一样。在途中，我们还以更基本的方式重建了椭圆形K3表面的模量压缩，Ascher-Bejleri，Ascher-Bejleri，Ascher-Bejleri，Alexeev-Brunyate-Engel，更加明确地分析了尖端。 我们还将Hein-Sun-Sun-Viaclovsky-Zhang的Hyperkahler纤维化为特殊情况，从我们的角度来看，在镜像对称环境中讨论其他情况以及与Landau-Ginzburg模型的可能关系。
A protagonist here is a new-type invariant for type II degenerations of K3 surfaces, which is explicit PL (piecewise linear) convex function from the interval with at most 18 non-linear points. Forgetting its actual function behaviour, it also classifies the type II degenerations into several combinatorial types, depending on the type of root lattices as appeared in classical examples. From differential geometric viewpoint, the function is obtained as the density function of the limit measure on the collapsing hyperKahler metrics to conjectural segments, as in the work of Honda-Sun-Zhang. On the way, we also reconstruct a moduli compactification of elliptic K3 surfaces in the works of Brunyate, Ascher-Bejleri, Alexeev-Brunyate-Engel in a more elementary manner, analyze the cusps more explicitly. We also interpret the glued hyperKahler fibration of Hein-Sun-Viaclovsky-Zhang as a special case from our viewpoint, discuss other cases, and possible relations with Landau-Ginzburg models in the mirror symmetry context.
