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arXiv · 0803.3337

The Canonical Model of a Singular Curve

Steven L. Kleiman·Renato V. Martins
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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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Steven L. Kleiman, Renato V. Martins. 2008-03-23. The Canonical Model of a Singular Curve. https://arxiv.org/abs/0803.3337

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