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On some Siegel threefold related to the tangent cone of the Fermat quartic surface

On some Siegel threefold related to the tangent cone of the Fermat quartic surface

Let $Z$ be the quotient of the Siegel modular threefold $\mathcal{A}^{\rm sa}(2,4,8)$ which has been studied by van Geemen and Nygaard. They gave an implication that some 6-tuple $F_Z$ of theta constants which is in turn known to be a Klingen type Eisenstein series of weight 3 should be related …