论文标题
calabi-yau振动，简单的K-等效性和突变
Calabi-Yau fibrations, simple K-equivalence and mutations
论文作者
论文摘要
均匀的屋顶是PICARD等级2和配备两个不同$ \ Mathbb P^{R-1} $捆绑结构的索引$ r $的合理种类。我们考虑在光滑的投影品种上考虑一束均匀的屋顶，制定了卡拉比二元性的相对版本 - YAU与投影捆绑包的屋顶相关的二元。我们讨论了这种对的衍生等效性如何提高到calabi-Yau纤维，从而将Bridgeland和maciocia的结果扩展到了较高的病例。我们制定了一种方法，以证明$ dk $ conconture适用于一类简单的$ k $ - 等效的地图，这是由屋顶捆绑的。例如，我们提出了一对八维的calabi-yau品种，在双calabi-yau中纤维三倍，与GLSM相变相关，我们证明与上述方法得出的等效性。
A homogeneous roof is a rational homogeneous variety of Picard rank 2 and index $r$ equipped with two different $\mathbb P^{r-1}$-bundle structures. We consider bundles of homogeneous roofs over a smooth projective variety, formulating a relative version of the duality of Calabi--Yau pairs associated to roofs of projective bundles. We discuss how derived equivalence of such pairs can lift to Calabi--Yau fibrations, extending a result of Bridgeland and Maciocia to higher-dimensional cases. We formulate an approach to prove that the $DK$-conjecture holds for a class of simple $K$-equivalent maps arising from bundles of roofs. As an example, we propose a pair of eight-dimensional Calabi--Yau varieties fibered in dual Calabi--Yau threefolds, related by a GLSM phase transition, and we prove derived equivalence with the methods above.
