A new complete Calabi–Yau metric on $${\mathbb {C}}^3$$C3
A new complete Calabi–Yau metric on $${\mathbb {C}}^3$$C3
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DOI：
10.1007/s00222-019-00861-w
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发表时间：
2017-05
影响因子：
3.1
通讯作者：
Yang Li
中科院分区：
文献类型：
--
作者：
Yang Li
受Lefschetz K3纤维化的Calabi-Yau 3-folds坍缩研究的启发，我们构造了一个完整的具有最大体积增长的Calabi-Yau度量，它在适当的尺度下有望模拟节点附近的坍缩度量.这种新的Calabi-Yau度量在无穷远处具有奇异的切锥，其黎曼几何在切锥的奇异性附近具有某些非标准特征，这些特征在绝热极限问题中更为典型.证明使用了H-J. Hein博士的一个存在性结果。论文的目的是将渐近近似解摄动为实际解，主要困难在于校正缓慢衰减的误差项。
Motivated by the study of collapsing Calabi–Yau 3-folds with a Lefschetz K3 fibration, we construct a complete Calabi–Yau metric onwith maximal volume growth, which in the appropriate scale is expected to model the collapsing metric near the nodal point. This new Calabi–Yau metric has singular tangent cone at infinity, and its Riemannian geometry has certain non-standard features near the singularity of the tangent cone, which are more typical of adiabatic limit problems. The proof uses an existence result in H-J. Hein’s Ph.D. thesis to perturb an asymptotic approximate solution into an actual solution, and the main difficulty lies in correcting the slowly decaying error terms.