The Canonical Model of a Singular Curve

Details The Canonical Model of a Singular Curve The Canonical Model of a Singular Curve

2008-03-23

arxiv.org/abs/0803.3337v1

Mathematics

Algebraic Geometry

28 pages, no figures, IV Congresso Iberoamericano de Geometria Complexa

Scientific paper

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 \omega. 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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