从平滑 Calabi-Yau 完全交点出发的完全 Calabi-Yau 度量

Pub Date : 2024-02-19 DOI:10.1007/s10711-024-00886-3

Benjy J. Firester

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引用次数: 0

摘要

我们构造了非紧凑流形上的完整卡拉比-尤（Calabi-Yau）度量，它们是一个卡拉比-尤锥的初始完整交集 \(V_0\)的平滑化，扩展了 Székelyhidi 的工作（《杜克大学数学学报》168(14):2651-2700, 2019）。所构造的卡拉比-尤流形在无穷远处的切锥是由\({\mathbb {C}}\times V_0\)给出的。这种构造产生的卡拉比优流形的纤维具有不同的复杂结构和可能的孤立奇点。

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Complete Calabi–Yau metrics from smoothing Calabi–Yau complete intersections

We construct complete Calabi–Yau metrics on non-compact manifolds that are smoothings of an initial complete intersection \(V_0\) that is a Calabi–Yau cone, extending the work of Székelyhidi (Duke Math J 168(14):2651–2700, 2019). The constructed Calabi–Yau manifold has tangent cone at infinity given by \({\mathbb {C}}\times V_0\). This construction produces Calabi–Yau metrics with fibers having varying complex structures and possibly isolated singularities.

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