Singular semi-flat Calabi-Yau metrics on \(S^2\) (Q812183)

The author obtains degenerate limits on a two-dimensional sphere equipped with a Riemannian metric with prescribed singularities at \(24\) points. The main result is Theorem 1. Given any holomorphic cubic differential \(U\) on \(\mathbb{C} P^1\) which has poles of order \(1\) at a finite number of points \(p_j\) and is not identically zero, there exists an affine flat structure and a semi-flat Calabi-Yau metric on \(\mathbb{C} P^1\backslash \{p_j\}\). The singularities of the affine flat structure and metric at the \(p_j\) are asymptotically the same as those in [\textit{M. Gross} and \textit{P. M. H. Wilson}, J. Differ. Geom. 55, 475--546 (2000; Zbl 1027.32021)].