Curves of genus whose canonical model lies on a surface of degree

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 be a non-hyperelliptic curve of genus . We prove that if the minimal degree of a surface containing the canonical model of in is , then either and carries exactly one or and 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

Email:
casnati@calvino.polito.it

DOI:
https://doi.org/10.1090/S0002-9939-2012-11335-8

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.