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A discrete extension of Γ_{1,p}^{\circ}(2) in SP(4,R) and the modular form of the Barth-Nieto quintic

Michael Friedland
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Abstract

We construct a maximal discrete extension of the paramodular group with a full level-2 structure. The corresponding Siegel variety parametrizes (birationally) the space of Kummer surfaces associated to (1,p)-polarized abelian surfaces with a level-2 structure. In the case p=3 this is related to the Barth-Nieto quintic and in this case we also determine the space of cusp forms of weight 3.

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Michael Friedland. 2002-11-13. A discrete extension of Γ_{1,p}^{\circ}(2) in SP(4,R) and the modular form of the Barth-Nieto quintic. https://arxiv.org/abs/math/0211208

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