The uniqueness of a fixed degree singular plane model


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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