论文标题
圆形$ k3 $ hypersurfaces和镜像对称性的椭圆形振动
Elliptic fibrations on toric $K3$ hypersurfaces and mirror symmetry derived from Fano polytopes
论文作者
论文摘要
我们确定了$ k3 $ hypersurfaces的néron-severi晶格，其中含有大量的紫红色数字三倍，来自fano polytopes。在每个$ k3 $的表面上，我们引入了特定的椭圆纤维。为了证明主定理的证明，我们表明每个$ k3 $表面的néron-severi晶格是由我们椭圆纤维奇异纤维的一般纤维，部分和适当选择的成分生成的。我们的论点提供了一定的证据，证明了Fano多面体的Dolgachev猜想，这是$ K3 $表面的镜子对称性的猜想。
We determine the Néron-Severi lattices of $K3$ hypersurfaces with large Picard number in toric three-folds derived from Fano polytopes. On each $K3$ surface, we introduce a particular elliptic fibration. In the proof of the main theorem, we show that the Néron-Severi lattice of each $K3$ surface is generated by a general fibre, sections and appropriately selected components of the singular fibres of our elliptic fibration. Our argument gives a certain proof of the Dolgachev conjecture for Fano polytopes, which is a conjecture on mirror symmetry for $K3$ surfaces.
