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

Chi Li

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

Differential Geometry 2013-05-28 v4 Mathematical Physics math.MP

Authors: Chi Li

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.

Keywords

kahler-einstein metric conical singularities numerical solutions projective plane so(3)-invariant cone angles

Cite

@article{arxiv.1207.6592,
  title  = {Numerical Solutions of Kahler-Einstein metrics on $P^2$ with conical singularities along a conic curve},
  author = {Chi Li},
  journal= {arXiv preprint arXiv:1207.6592},
  year   = {2013}
}

Comments

20 pages. 7 figures. v3: The limit behavior and bubbling are studied numerically. More detailed calculations and numerical studies are added. The relation with previous work are discussed. Codes for generating the graphs are added. v4: Many typos are corrected. Some signs slightly modified to maintain consistence

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

Abstract

Keywords

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