Mixed cusp forms and holomorphic forms on elliptic varieties
Let \(E^m\) be an elliptic variety, that means the resolution of the singularities of the \(m\)-times fibre product \(E\times_{\pi}\dots\times_{\pi}E\to X\) of an elliptic fibration \(\pi: E\to X\). The author generalizes the results for elliptic surface \((m=1)\) [see \textit{B. Hunt} and \textit{W. Meyer}, Math. Ann. 271, 53--80 (1985; Zbl 0533.14019)] by defining mixed cusp forms associated to \(E^m\) and proving that the space of these mixed cusp forms coincides with the space of holomorphic \((m+1)\)-forms on \(E^m\). Thus he succeeds in determining the geometric genus of \(E^m\) under certain conditions.
scientific article; zbMATH DE number 4057671