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Preprints, Working Papers, ... Year : 2024

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

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 for asymptotically conical Calabi-Yau manifolds in the sense of Conlon-Hein.
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Dates and versions

hal-04428381 , version 1 (31-01-2024)

Identifiers

  • HAL Id : hal-04428381 , version 1

Cite

Tran-Trung Nghiem. Calabi-Yau metrics on rank two symmetric spaces with horospherical tangent cone at infinity. 2024. ⟨hal-04428381⟩
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