Canonical curves on surfaces of very low degree

Author:
G. Casnati

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

Published electronically:
July 29, 2011

MathSciNet review:
2869104

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a non-hyperelliptic curve of genus . We recall some facts about curves endowed with a base-point-free . Then we prove that if the minimal degree of a surface containing the canonical model of in is , then and carries exactly one . As a by-product, we deduce that if the canonical model of in is contained in a surface of degree at most , then 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

Email:
casnati@calvino.polito.it

DOI:
https://doi.org/10.1090/S0002-9939-2011-10979-1

Keywords:
Curve,
canonical model,
tetragonality,
Maroni number,
apolarity.

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 ’Geometria delle varieté a algebriche e dei loro spazi di moduli’, cofinanced by MIUR (COFIN 2008)

Communicated by:
Lev Borisov

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.