Hans-Joachim Hein: A gluing construction for complex surfaces with hyperbolic cusps

Date: 2023-07-13

Time: 11:20 - 12:00


Hans-Joachim Hein, WWU Münster


We will describe an example of a degeneration of degree 6 algebraic surfaces in CP^3 with only ordinary triple point singularities 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 points, (2) long thin neck regions, and (3) Tian-Yau’s complete Ricci-flat Kähler metrics in small neighborhoods of the vanishing cycles.

Joint work with Xin Fu and Xumin Jiang.