The Canonical Model of a Singular Curve

• Main Authors: Kleiman, Steven L. (Contributor), Vidal Martins, Renato (Author)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: Springer, 2011-05-18T21:06:22Z.
• Subjects: Article
• Online Access: Get fulltext

We give re fined statements and modern proofs of Rosenlicht's re- sults 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.
Conselho Nacional de Pesquisas (Brazil) (Grant number PDE 200999/2005-2)