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Let be the stack of stable curves of genus with a given dual graph and let be its closure in . We consider the normalization of in order to classify the residual orbifolds of the normalizations of the irreducible components of the locus in corresponding to curves with at least nodes.
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Dan Edidin, Damiano Fulghesu, Normalization of the 1-stratum of the moduli space of stable curves. Port. Math. 69 (2012), no. 3, pp. 167–192DOI 10.4171/PM/1912