English

Some remarks to a Theorem of van Geemen

Algebraic Geometry 2025-04-01 v2 Number Theory

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 θm4\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 ϑ[m]k\vartheta[m]^k. We will show that k=4k=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

Keywords

Cite

@article{arxiv.2501.15213,
  title  = {Some remarks to a Theorem of van Geemen},
  author = {Riccardo Salvati Manni and Eberhard Freitag},
  journal= {arXiv preprint arXiv:2501.15213},
  year   = {2025}
}