Let be a projective curve either reduced with planar singularities or contained in a smooth algebraic surface. We show that the canonical ring is generated in degree 1 if is 3-connected and not (honestly) hyperelliptic; we show moreover that is generated in degree 1 if is reduced with planar singularities and is an invertible sheaf such that for every .
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Marco Franciosi, Elisa Tenni, The canonical ring of a 3-connected curve. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 25 (2014), no. 1, pp. 37–51DOI 10.4171/RLM/667