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Published online by Cambridge University Press: 22 January 2016
In § 1 of this note we construct abelian varieties of dimension two defined over Fpn, n odd, which admit infinitely many distinct principal polarizations. These polarizations determine an infinite family of geometrically non-isomorphic complete singular curves defined and irreducible over Fpn which have isomorphic Jacobian varieties. In § 2 we calculate the zeta function of these curves.