2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153901The family hyperbolic metric for the plumbing variety $\{zw=t\}$ and the non holomorphic Eisenstein series $E(ζ;2)$ are combined to provide an explicit expansion for the hyperbolic metrics for degenerating families of Riemann surfaces. Applications include an asymptotic expansion for the Weil-Petersson metric and a local form of symplectic reduction.Published in Mathematischen Annalen, 2008. The original publication is available at http://www.springerlink.comComplex VariablesAlgebraic Geometry32G15; 32Q15; 30F60; 53D30text