A gluing construction for complex surfaces with hyperbolic cusps

13.02.2025, 10:00  –  Hörsaal in Haus 10
Forschungsseminar Differentialgeometrie

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.