Hans-Joachim Hein (Münster)
We will describe an example of a degeneration of degree 6 algebraic surfaces in \(\mathbb{CP}^3\) with an isolated triple point singularity on its central fiber. Then we will show how the unique negative Kähler-Einstein metrics on the smooth fibers, which exist by the Aubin-Yau theorem, disintegrate into three distinct geometric pieces on approach to the central fiber:
(1) Kobayashi's complete Kähler-Einstein metric on the complement of the triple point,
(2) long thin neck regions, and
(3) Tian-Yau's complete Ricci-flat Kähler metric in small neighborhoods of the vanishing cycles.
Joint work with Xin Fu and Xumin Jiang.
