A Note on a Brill-Noether Locus over a Non-hyperelliptic curve of genus 4

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We prove that a certain Brill-Noether locus over a non-hyperelliptic curve $C$ of genus 4, is isomorphic to the \textit{Donagi-Izadi cubic threefold} in the case when the pencils of the two trigonal line bundles of $C$ coincide.
8 pages, sort of appendix to the article [arxiv:0810.4392], any comments welcome

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