Degenerations of negative Kähler–Einstein surfaces

Abstract

AbstractEvery compact Kähler manifold with negative first Chern class admits a unique metric such that . Understanding how families of these metrics degenerate gives insight into their geometry and is important for understanding the compactification of the moduli space of negative Kähler–Einstein metrics. I study a special class of such families in complex dimension two. Following the work of Sun and Zhang in the Calabi–Yau case [2019, arXiv:1906.03368], I construct a Kähler–Einstein neck region interpolating between canonical metrics on components of the central fiber. This provides a model for the limiting geometry of metrics in the family.