Calabi-Yau metrics with cone singularities along intersecting complex lines: the unstable case
arXiv:2006.06065 · doi:10.1112/jlms.12558
Abstract
We produce local Calabi-Yau metrics on with conical singularities along three or more complex lines through the origin whose cone angles strictly violate the Troyanov condition. The tangent cone at the origin is a flat polyhedral Kähler cone with conical singularities along two intersecting lines: one with cone angle corresponding to the line with smallest cone angle, while the other forms as the collision of the remaining lines into a single conical line. Using a branched covering argument, we can construct Calabi-Yau metrics with cone singularities along cuspidal curves with cone angle in the unstable range.
Final version. Accepted in the Journal of the London Mathematical Society