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arXiv · 2401.05122

Calabi-Yau metrics on rank two symmetric spaces with horospherical tangent cone at infinity

Tran-Trung Nghiem
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Abstract

We show that on every non-$G_2$ complex symmetric space of rank two, there are complete Calabi-Yau metrics of Euclidean volume growth with prescribed horospherical singular tangent cone at infinity, providing the first examples of affine Calabi-Yau smoothings of singular and irregular tangent cone. As a corollary, we obtain infinitely many examples of Calabi-Yau manifolds degenerating to the tangent cone in a single step, supporting a recent conjecture by Sun-Zhang, which was only proved when the tangent cone at infinity has only an isolated singularity.

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Tran-Trung Nghiem. 2024-01-10. Calabi-Yau metrics on rank two symmetric spaces with horospherical tangent cone at infinity. https://doi.org/10.4310/jdg%2F1779981710

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