Lines on some Calabi-Yau threefolds in \(\mathbb {P}^4\) (Q2255138)

The author studies some hypersurfaces in \(\mathbb{P}^{4}\), whose normalizations is a Calabi-Yau threefold. Then, the lines on these normalizations are examined. More explicitly, the author extends the constructions of Ciliberto to the canonical surfaces of degree \(d=6\) in \(\mathbb{P}^{4}\). The author also includes some work on \(d=10\) case considering quasi étale double coverings of general determinantal symmetric quintics.