Hyperbolic 2-spheres with conical singularities, accessory parameters and Kähler metrics on {{ℳ}}_{0,}
Hyperbolic 2-spheres with conical singularities, accessory parameters and Kähler metrics on {{ℳ}}_{0,}
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{{ℳ}}_{0,} 上具有圆锥奇点、辅助参数和 Kähler 度量的双曲 2-球体
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
P. Zograf
中科院分区：
文献类型：
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作者：
L. Takhtajan;P. Zograf
We show that the real-valued function S α on the moduli space M 0,n of pointed rational curves, defined as the critical value of the Liouville action functional on a hyperbolic 2-sphere with n ≥ 3 conical singularities of arbitrary orders α = {α 1 ,...,α n }, generates accessory parameters of the associated Fuchsian differential equation as their common antiderivative. We introduce a family of Kahler metrics on M 0,n parameterized by the set of orders a, explicitly relate accessory parameters to these metrics, and prove that the functions S α are their Kahler potentials.
