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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Curves of genus $g$ whose canonical model lies on a surface of degree $g+1$
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by Gianfranco Casnati PDF
Proc. Amer. Math. Soc. 141 (2013), 437-450 Request permission


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:
  • 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
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 437-450
  • MSC (2010): Primary 14N25; Secondary 14H51, 14H30, 14N05
  • DOI:
  • MathSciNet review: 2996948