Submission date: 11 February 2018

Abstract:

We study Gromov-Hausdorff limits of complex curves with singular flat metrics and show that the limit of a maximally degenerate family of such curves is a metric graph which is homeomorphic to a quotient of a skeleton of the associated Berkovich analytic space with respect to a semi-stable vertex set.

Mathematics Subject Classification:

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Full text arXiv 1802.03818: pdf, ps.