English

Grafting hyperbolic metrics and Eisenstein series

Complex Variables 2008-02-04 v2 Algebraic Geometry

Abstract

The family hyperbolic metric for the plumbing variety {zw=t}\{zw=t\} and the non holomorphic Eisenstein series E(ζ;2)E(\zeta;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.

Keywords

Cite

@article{arxiv.0704.3169,
  title  = {Grafting hyperbolic metrics and Eisenstein series},
  author = {Kunio Obitsu and Scott A. Wolpert},
  journal= {arXiv preprint arXiv:0704.3169},
  year   = {2008}
}
R2 v1 2026-06-21T08:21:37.101Z