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Curves of genus $ g$ whose canonical model lies on a surface of degree $ g+1$

Author: Gianfranco Casnati
Journal: Proc. Amer. Math. Soc. 141 (2013), 437-450
MSC (2010): Primary 14N25; Secondary 14H51, 14H30, 14N05
Published electronically: June 12, 2012
MathSciNet review: 2996948
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Abstract: Let $ C$ be a non-hyperelliptic curve of genus $ g$. We prove that if the minimal degree of a surface containing the canonical model of $ C$ in $ \check {\mathbb{P}}_k^{g-1}$ is $ g+1$, then either $ g\ge 9$ and $ C$ carries exactly one $ g^{1}_{4}$ or $ 7\le g\le 15$ and $ C$ is birationally isomorphic to a plane septic curve with at most double points as singularities.

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Additional Information

Gianfranco Casnati
Affiliation: Dipartimento di Matematica, Politecnico di Torino, c. so Duca degli Abruzzi 24, 10129 Torino, Italy

Keywords: Curve, canonical model, tetragonality.
Received by editor(s): March 21, 2011
Received by editor(s) in revised form: July 1, 2011
Published electronically: June 12, 2012
Additional Notes: This work was done in the framework of PRIN ‘Geometria delle varietà algebriche e dei loro spazi di moduli’, cofinanced by MIUR (COFIN 2008)
Communicated by: Lev Borisov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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