Lines on the Dwork pencil of quintic threefolds
Lines on the Dwork pencil of quintic threefolds
We present an explicit parameterization of the families of lines of the Dwork pencil of quintic threefolds. This gives rise to isomorphic curves $\widetilde{C}_{\pm \varphi}$, which parameterize the lines. These curves are 125:1 covers of genus six curves $C_{\pm \varphi }$. The $C_{\pm \varphi}$ are first presented as curves in …