Geodesic
Canonical maps of pointed nodal curves
Sbornik. Mathematics, Tome 195 (2004) no. 5, pp. 615-642 
I. V. Artamkin. Canonical maps of pointed nodal curves. Sbornik. Mathematics, Tome 195 (2004) no. 5, pp. 615-642. http://geodesic.mathdoc.fr/item/SM_2004_195_5_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In 1983 Knudsen proved that the triple-canonical map of a pointed Deligne–Mumford stable curve is an embedding, and the double-canonical map has no base points. The same question is discussed here for the canonical map. The answer can be stated virtually purely topologically in terms of the dual graph, with the exception of the case of hyperelliptic curves.

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