Boundary asymptotics of the relative Bergman kernel metric for elliptic curves II: subleading terms
Volume 118 / 2016
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
Abstract
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.
