English

Small angle limits of negatively curved Kahler-Einstein metrics with crossing edge singularities

Differential Geometry 2021-01-22 v1

Abstract

Let (X,D)(X, D) be a log smooth log canonical pair such that KX+DK_X+D is ample. Extending a theorem of Guenancia and building on his techniques, we show that negatively curved K\"{a}hler-Einstein crossing edge metrics converge to K\"{a}hler-Einstein mixed cusp and edge metrics smoothly away from the divisor when some of the cone angles converge to 00. We further show that near the divisor such normalized K\"{a}hler-Einstein crossing edge metrics converge to a mixed cylinder and edge metric in the pointed Gromov-Hausdorff sense when some of the cone angles converge to 00 at (possibly) different speeds.

Keywords

Cite

@article{arxiv.2101.08404,
  title  = {Small angle limits of negatively curved Kahler-Einstein metrics with crossing edge singularities},
  author = {Yuxiang Ji},
  journal= {arXiv preprint arXiv:2101.08404},
  year   = {2021}
}