We analyse line bundle cohomologies on all favourable co‐dimension two Complete Intersection Calabi Yau (CICY) manifolds of Picard number two. Our results provide further evidence that the cohomology dimensions of such line bundles are given by analytic expressions, which change between regions in the line bundle charge space. This agrees with recent observations of CY line bundles presented in Refs. [1, 2]. In many cases, the expressions for bundle cohomology dimensions are polynomial functions of the line bundle charges (of degree at most 3), and the regions are cones. A more novel observation is that for some CICY manifolds, the cohomologies are more succinctly determined by recursive relationships. There can also be boundaries between regions where a polynomial fit fails, and we link these exceptional cases to irregular behaviour of the index of the line bundle. Finally, our observations provide evidence for similarities in the line bundle cohomologies for CICY manifolds that share rows in the configuration matrix. Among such related CICY manifolds, we find both that the line bundle charge space is partitioned in the same manner, and that the same, or closely related, analytical descriptions apply for the cohomology dimensions in these regions.

中文翻译：

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具有Picard第二号的CICY上的线束同调

我们分析了第二个皮卡德的所有有利维数两个完整交集卡拉比丘（CICY）流形上的线束同调。我们的结果提供了进一步的证据，即这种线束的同调维数是由解析表达式给出的，解析表达式在线束电荷空间的各个区域之间变化。这与参考文献中对CY线束的最新观察结果一致。[1，2]。在许多情况下，束同调维数的表达式是线束电荷（度数最多为3）的多项式函数，而区域是圆锥体。一个更新颖的发现是，对于某些CICY流形，通过递归关系更简洁地确定了同调。多项式拟合失败的区域之间也可能存在边界，并将这些例外情况与线束索引的不规则行为联系起来。最后，我们的观察结果为共享配置矩阵中行的CICY流形线束同调的相似性提供了证据。在这些相关的CICY流形中，我们发现线束电荷空间以相同的方式划分，并且相同或紧密相关的分析描述适用于这些区域中的同调维度。