Hyperbolic 2-spheres with conical singularities, accessory parameters and Kaehler metrics on $\mathcal{M}_{0,n}$

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dc.creatorTakhtajan, Leon
dc.creatorZograf, Peter
dc.date2001-12-17
dc.date.accessioned2026-07-07T04:45:18Z
dc.date.available2026-07-07T04:45:18Z
dc.descriptionWe show that the real-valued function $S_α$ on the moduli space $\mathcal{M}_{0,n}$ of pointed rational curves, defined as the critical value of the Liouville action functional on a hyperbolic 2-sphere with $n\geq 3$ 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 Kaehler metrics on $\mathcal{M}_{0,n}$ parameterized by the set of orders $α$, explictly relate accessory parameters to these metrics, and prove that the functions $S_α$ are their Kaehler potentials.
dc.descriptionAMS LaTex, 13 pages
dc.identifierhttps://arxiv.org/abs/math/0112170
dc.identifierhttp://arxiv.org/abs/math/0112170
dc.identifierTrans. Amer. Math. Soc. 355 (2003), no. 5, 1857--1867
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62904
dc.subjectComplex Variables
dc.subjectHigh Energy Physics - Theory
dc.subjectDifferential Geometry
dc.subject14H15 (Primary) 30F45, 81T40 (Secondary)
dc.titleHyperbolic 2-spheres with conical singularities, accessory parameters and Kaehler metrics on $\mathcal{M}_{0,n}$
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