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arXiv · 2501.15213

Some remarks to a Theorem of van Geemen

Riccardo Salvati Manni·Eberhard Freitag
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Abstract

In [ Ge], Bert van Geemen computed the dimension of the space of the fourth power of the theta nullwerte. In [SM2], it has been observe that all linear relations between the $\theta_m^4$ are consequences of the quartic Riemann relations. In this note, we want to give a new proof of these result and extend them. In a last section we treat the linear dependencies between arbitrary powers $\vartheta[m]^k$. We will show that $k=4$ is the only case where such dependencies can occur. For this reason, we give a slightly different title: Some remarks to a Theorem of van Geemen

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Riccardo Salvati Manni, Eberhard Freitag. 2025-01-25. Some remarks to a Theorem of van Geemen. https://arxiv.org/abs/2501.15213

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