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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
DOI: https://doi.org/10.1090/S0002-9939-2012-11335-8
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
MR Author ID: 313798
Email: casnati@calvino.polito.it

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.