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The canonical model of a singular curve

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Abstract

We give refined statements and modern proofs of Rosenlicht’s results about the canonical model C′ of an arbitrary complete integral curve C. Notably, we prove that C and C′ are birationally equivalent if and only if C is nonhyperelliptic, and that, if C is nonhyperelliptic, then C′ is equal to the blowup of C with respect to the canonical sheaf ω. We also prove some new results: we determine just when C′ is rational normal, arithmetically normal, projectively normal, and linearly normal.

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Authors and Affiliations

  1. Department of Mathematics, 2-278 MIT, 77 Mass. Avenue, Cambridge, MA, 02139, USA

    Steven Lawrence Kleiman

  2. Departamento de Matemática, ICEx, UFMG, Av. Antônio Carlos 6627, 30123-970, Belo Horizonte, MG, Brazil

    Renato Vidal Martins

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  1. Steven Lawrence Kleiman
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  2. Renato Vidal Martins
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Correspondence to Steven Lawrence Kleiman.

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Kleiman, S.L., Martins, R.V. The canonical model of a singular curve. Geom Dedicata 139, 139–166 (2009). https://doi.org/10.1007/s10711-008-9331-4

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  • DOI: https://doi.org/10.1007/s10711-008-9331-4

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