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Boundary asymptotics of the relative Bergman kernel metric for elliptic curves II: subleading terms

Volume 118 / 2016

Robert Xin Dong Annales Polonici Mathematici 118 (2016), 59-69 MSC: Primary 32A25; Secondary 32G15, 14D06, 30F45. DOI: 10.4064/ap3841-8-2016 Published online: 7 October 2016


For a Legendre family of elliptic curves near the moduli space boundary, we study asymptotic behavior at a node of the relative Bergman kernel metric and show that its curvature form coincides with the Poincaré metric of $\mathbb C\setminus \{0, 1\}$. Four-term and three-term asymptotic expansion formulas near $0$ are obtained for this metric and its Kähler potential, respectively.


  • Robert Xin DongGraduate School of Mathematics
    Nagoya University
    464-8602 Nagoya, Japan

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