2024/01/10 by Nghiem, Tran-Trung · 1 citation
#14M27 #32Q25 #53C25 #53C55 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2401.05122
We show that on every non-G2 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.