论文标题
calabi-yau流形的新的反式Torelli定理的反示例
New counterexamples to the birational Torelli theorem for Calabi--Yau manifolds
论文作者
论文摘要
我们对calabi-yau歧管的Birational Torelli定理进行反例，以任意高维度：这是通过展示一系列非偶然的Calabi-yau $（n^2-1）$ - 折叠来完成的。这些品种还满足了Grothendieck品种环中的$ \ Mathbb l $ - 等效关系，即它们的类别的差异可以消灭仿期线的类别。我们陈述了一个更广泛的卡拉比（Calabi-Yau）对的最后一个财产，即所有那些被认为是一般$（1,1）$的全部属性的属性（在卡内米苏（Kanemitsu）的意义上，沿其两个极端宫缩，在同质屋顶上。
We produce counterexamples to the birational Torelli theorem for Calabi-Yau manifolds in arbitrarily high dimension: this is done by exhibiting a series of non birational pairs of Calabi-Yau $(n^2-1)$-folds which, for $n \geq 2$ even, admit an isometry between their middle cohomologies. These varieties also satisfy an $\mathbb L$-equivalence relation in the Grothendieck ring of varieties, i.e. the difference of their classes annihilates a power of the class of the affine line. We state this last property for a broader class of Calabi-Yau pairs, namely all those which are realized as pushforwards of a general $(1,1)$-section on a homogeneous roof in the sense of Kanemitsu, along its two extremal contractions.
