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The Riemann theta function for a genus $g$ closed Riemann surface with period matrix $\tau=[\tau_{ij}]$ is defined by $$\theta(\{z_1,\cdots,z_g\}|\tau)=\Sigma_{n\in\mathbb{Z}^g}e^{\pi i(n\cdot\tau\...

1) Is there a (simple) way to characterise the convergence of complex curves toward a stable curve in term of hyperbolic metrics for the Deligne Mumford compactification of the moduli space of complex ...