一族紧的复辛非kähler Calabi-Yau流形
A Family of Compact Complex-Symplectic Calabi-Yau Manifolds that are Nonkähler
摘要：
构造了一族$6$维紧致流形$M(A)$，它们同时与复Calabi-Yau流形和辛Calabi-Yau流形同构.它们具有基本群$\mathbb{Z} \oplus \mathbb{Z}$，它们的奇维贝蒂数是偶数，它们满足硬Lefschetz性质，它们的实同伦类型是形式的.然而，对于任何拓扑空间$Y$，$M(A) \times Y$不是同伦等价于任何紧Kähler流形。
英文摘要：
We construct a family of $6$-dimensional compact manifolds $M(A)$, which are simultaneously diffeomorphic to complex Calabi-Yau manifolds and symplectic Calabi-Yau manifolds. They have fundamental groups $\mathbb{Z} \oplus \mathbb{Z}$, their odd-dimensional Betti numbers are even, they satisfy the hard Lefschetz property, and their real homotopy types are formal. However, $M(A) \times Y$ are not homotopy equivalent to any compact Kähler manifold for any topological space $Y$.
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