AI 中文总结
本文构造了锥形流形小解消上具有最大体积增长的完整Calabi-Yau度量族，其退化收敛到带锥形奇点的度量，实现了Atiyah翻转。
AI 中文摘要
我们在锥形流形 $\mathcal{Z} = \{z_1^2 + z_2^2 + z_3^2 + z_4^2 = 0\} \subset \mathbb{C}^4$ 的小解消上构造了具有最大体积增长的完整Calabi-Yau度量的新族。这些度量在无穷远处具有切锥 $\mathbb{C} \times (\mathbb{C}^2 / \mathbb{Z}_2)$，并由其Kähler类参数化。当Kähler类退化时，度量在尖点Gromov-Hausdorff意义下收敛到 $\mathcal{Z}$ 上的一个Calabi-Yau度量，该度量在普通双点处具有以Stenzel度量为模型的孤立锥形奇点，且在无穷远处切锥为 $\mathbb{C} \times (\mathbb{C}^2/\mathbb{Z}_2)$，从而为Atiyah翻转提供了新的度量实现。
英文摘要
We construct new families of complete Calabi-Yau metrics with maximal volume growth on the small resolutions of the conifold $\mathcal{Z} = \{z_1^2 + z_2^2 + z_3^2 + z_4^2 = 0\} \subset \mathbb{C}^4$. These metrics have tangent cone $\mathbb{C} \times (\mathbb{C}^2 / \mathbb{Z}_2)$ at infinity and are parametrised by their Kähler class. As the Kähler class degenerates, the metrics converge in the pointed Gromov-Hausdorff sense to a Calabi-Yau metric on $\mathcal{Z}$ with an isolated conical singularity modelled on the Stenzel metric at the ordinary double point and tangent cone at infinity $\mathbb{C} \times (\mathbb{C}^2/\mathbb{Z}_2)$, thereby providing a new metric realisation of the Atiyah flop.
Comments65 pages, 1 appendix. Comments are welcome!
