The Canonical Model of a Singular Curve
Name
Kleiman Geometriae Dedicata.pdf
Size
219.21 KB
Format
Adobe PDF
Checksum (MD5)
a58c377fc6766d7d43f2e7e2cbee93c2
Author(s)
Kleiman, Steven L.
Vidal Martins, Renato
Date Issued
April 2009
Journal
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
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10711-008-9331-4
