The Göpel Variety

ABSTRACT

In this paper, we will prove that the six-dimensional Göpel variety in P¹³⁴ is generated by 120 linear, 35 cubic, and 35 quartic relations. This result was already obtained in [Ren et al. 13], but the authors used a statement in [Coble 29] saying that the Göpel variety set theoretically is generated by the linear and cubic relations alone. Unfortunately this statement is false. There are 120 extra points. Nevertheless the results stated in [Ren et al. 13] are correct. There are required several changes that we will illustrate in some detail.

KEYWORDS:

• Göpel variety
• moduli space
• thetanullwerte
• modular forms

MATHEMATICS SUBJECT CLASSIFICATION:

• 14J15