The Canonical Model of a Singular Curve
Algebraic Geometry
2008-03-25 v1
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 \omega. We also prove some new results: we determine just when C' is rational normal, arithmetically normal, projectively normal, and linearly normal.
Keywords
Cite
@article{arxiv.0803.3337,
title = {The Canonical Model of a Singular Curve},
author = {Steven L. Kleiman and Renato V. Martins},
journal= {arXiv preprint arXiv:0803.3337},
year = {2008}
}
Comments
28 pages, no figures, IV Congresso Iberoamericano de Geometria Complexa