Some remarks to a theorem of van Geemen

Bert van Geemen computed the dimension of the space of the fourth power of the thetanullwerte. In [7], it has been observed that all linear relations are consequences of the quartic Riemann relations. In this note, we want to give a new proof of these results and extend them. to the vector valued case. In a last section we treat the linear dependencies between arbitrary powers of the thetanullwerte. We will show that k = 4 is the only case where such dependencies can occur.