Abstract
Given a finite collection of lines $L_j \subset \mathbb{CP}^2$ together with real numbers $0 \lt \beta_j \lt 1$ satisfying natural constraint conditions, we show the existence of a Ricci–flat Kähler metric $g_{RF}$ with cone angle $2\pi\beta_j$ along each line $L_j$ asymptotic to a polyhedral Kähler cone at each multiple point. Moreover, we discuss a Chern–Weil formula that expresses the energy of $g_{RF}$ as a logarithmic Euler characteristic with points weighted according to the volume density of the metric.
Citation
Martin de Borbon. Cristiano Spotti. "Calabi–Yau metrics with conical singularities along line arrangements." J. Differential Geom. 123 (2) 195 - 239, February 2023. https://doi.org/10.4310/jdg/1680883576
Information