Numerical Solutions of Kahler-Einstein metrics on $P^2$ with conical singularities along a conic curve

Abstract

We solve for the SO(3)-invariant Kahler-Einstein metric on $\mathbb{P}^2$ with cone singularities along a smooth conic curve using numerical approach. The numerical results show the sharp range of angles ($(\pi/2,2\pi]$) for the solvability of equations, and the right limit metric space ($P(1,1,4)$). These results exactly match our theoretical conclusions.