The uniqueness of a fixed degree singular plane model

doi:10.1285/i15900932v44n1p21

The uniqueness of a fixed degree singular plane model

Edoardo Ballico

Abstract

Let $X$ be the normalization of an integral degree $d\ge 9$ plane curve $Y$ . We prove that $X$ has a unique $g^2_d$ if $h^1(\mathbb{P}^2,\mathcal{I}_Z(\lceil d/2\rceil -3))=0$ , where $Z$ is the conductor of $Y$ . Moreover, $Y$ is the unique plane model of $X$ of degree at most $d$ .

DOI Code: 10.1285/i15900932v44n1p21

Keywords: plane curve; uniqueness of a plane model

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Note di Matematica

The uniqueness of a fixed degree singular plane model

Abstract