论文标题
界限Kreuzer-Skarke景观
Bounding the Kreuzer-Skarke Landscape
论文作者
论文摘要
我们通过构造和计算反身多位式的三角剖分，研究了具有较大霍奇数字的卡拉比野三倍。通过计数相关的次级多面体中的计数点，我们表明，Kreuzer-Skarke列表中多台面的细，常规的，星形三角剖分的数量在上面由$ \ binom {14,111} {494} {494} {494} {494} \ 10^{928} $。适应Anclin对晶格多边形的三角剖分的结果，我们获得了列表中每个多层每个2面的三角形数量的结合。通过这种方式，我们证明，拓扑不相等的卡拉比YAU高空曲面由Kreuzer-Skarke列表引起的列表上以上限制为$ 10^{428} $。我们引入了有效的算法，用于构建Calabi-yau Hypersurfaces的代表性集合，包括极端情况$ H^{1,1} = 491 $，我们研究其中拓扑和物理数据的分布。最后，我们证明，一旦三角剖分按次级多层编码，神经网络可以准确预测这些数据。
We study Calabi-Yau threefolds with large Hodge numbers by constructing and counting triangulations of reflexive polytopes. By counting points in the associated secondary polytopes, we show that the number of fine, regular, star triangulations of polytopes in the Kreuzer-Skarke list is bounded above by $\binom{14,111}{494} \approx 10^{928}$. Adapting a result of Anclin on triangulations of lattice polygons, we obtain a bound on the number of triangulations of each 2-face of each polytope in the list. In this way we prove that the number of topologically inequivalent Calabi-Yau hypersurfaces arising from the Kreuzer-Skarke list is bounded above by $10^{428}$. We introduce efficient algorithms for constructing representative ensembles of Calabi-Yau hypersurfaces, including the extremal case $h^{1,1}=491$, and we study the distributions of topological and physical data therein. Finally, we demonstrate that neural networks can accurately predict these data once the triangulation is encoded in terms of the secondary polytope.
