The Canonical Model of a Singular Curve
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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.
Date issued
2009-04Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Geometriae Dedicata
Publisher
Springer
Citation
Kleiman, Steven Lawrence, and Renato Vidal Martins. “The canonical model of a singular curve.” Geometriae Dedicata 139.1 (2009) : 139-166. Copyright © 2009, Springer
Version: Author's final manuscript
ISSN
0046-5755