Van Geemen's families of lines on special quintic threefolds (Q1173741)

The authors study the family of lines on the quintic threefold of the Dwork pencil \(x^ 5_ 0+x^ 5_ 1+x^ 5_ 2+x^ 5_ 3+x^ 5_ 4-5tx_ 0x_ 1x_ 2x_ 3x_ 4=0\). They show (in a very explicit way) that on a generic threefold of the pencil there is a 1-dimensional family of lines that is not a cone. --- Part of the results are due to \textit{B. van Geemen}.