开Calabi-Yau流形的形变族与Stein性质
Deformation families of open Calabi-Yau manifolds and Steinness
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中文总结 AI 辅助
本文构造开Calabi-Yau流形的可紧化形变族，证明其非Stein性，并讨论与Brunella猜想相关的爆破CP2非Stein性及Stein纤维形变族。
中文摘要 AI 辅助
本文旨在构造开Calabi-Yau流形的形变族，并讨论其Stein性质。首先，我们构造了一个非平凡的可紧化开Calabi-Yau流形形变。其次，我们构造了一个具有全纯对合的可紧化形变族，并断言所有构造的可紧化形变族均非Stein。最后，我们讨论了与Macro Brunella猜想相关的CP2在九点爆破后的拟射影簇的非Stein性质，并给出了纤维为Stein的形变族。
英文摘要
This paper is to construct deformation families of open Calabi-Yau manifolds together with some discussions on Steinness. Firstly, we construct a nontrivial compactifiable deformation of open Calabi-Yau manifolds from rational elliptic surface with global sections. Secondly, we give a condition for the existence of an elliptic fibration with global sections on the complex analytic family of rational elliptic surface with global sections, construct a holomorphic involution on the compactifiable deformation family and claim the non-Steinness for all the compactifiable deformation families constructed. Finally, we give some discussions on the non-Steinness of the quasi-projective variety from $\text{CP}^2 \text{$\#$9} \overline{\text{CP}}^2$ corresponding to a conjecture by Marco Brunella and construct deformation families whose fibers were conjectured to be Stein by Andreas Höring and Thomas Peternel.
发表机构
- SYSU（中山大学）
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