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 $\dualp{g-1}$ is $g+1$, then either $g\ge9$ and $C$ carries exactly one $g^1_4$, or $7\le g\le15$ and $C$ is birationally isomorphic to a plane septic with at most double points as singularities.

Curves of genus g whose canonical model lies on a surface of degree g+1 / Casnati, Gianfranco. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - STAMPA. - 141:2(2013), pp. 437-450. [10.1090/S0002-9939-2012-11335-8]

Curves of genus g whose canonical model lies on a surface of degree g+1

CASNATI, GIANFRANCO
2013

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 $\dualp{g-1}$ is $g+1$, then either $g\ge9$ and $C$ carries exactly one $g^1_4$, or $7\le g\le15$ and $C$ is birationally isomorphic to a plane septic with at most double points as singularities.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2428186
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