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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Canonical curves on surfaces of very low degree
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by G. Casnati PDF
Proc. Amer. Math. Soc. 140 (2012), 1185-1197 Request permission

Abstract:

Let $C$ be a non–hyperelliptic curve of genus $g$. We recall some facts about curves endowed with a base–point–free $g^{1}_{4}$. Then we prove that if the minimal degree of a surface containing the canonical model of $C$ in $\check {\mathbb {P}}^{g-1}_k$ is $g$, then $7\le g\le 12$ and $C$ carries exactly one $g^{1}_{4}$. As a by–product, we deduce that if the canonical model of $C$ in $\check {\mathbb {P}}^{g-1}_k$ is contained in a surface of degree at most $g$, then $C$ is either trigonal or tetragonal or isomorphic to a plane sextic.
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Additional Information
  • G. 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
  • Received by editor(s): October 14, 2010
  • Received by editor(s) in revised form: December 15, 2010, December 26, 2010, and December 29, 2010
  • Published electronically: July 29, 2011
  • Additional Notes: This work was done in the framework of PRIN \lq Geometria delle varietĂ© a algebriche e dei loro spazi di moduli\rq, cofinanced by MIUR (COFIN 2008)
  • Communicated by: Lev Borisov
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1185-1197
  • MSC (2010): Primary 14N25; Secondary 14H51, 14H30, 14N05
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10979-1
  • MathSciNet review: 2869104