  Using the global Gulliksen-Neg{\aa}rd complex, we build in this note regular
canonical surfaces of general type in ${\mathbb P}^6$, Calabi-Yau 3-folds in
${\mathbb P}^7$ and Fano anticanonical 4-folds, all of degree 17 and 20. We
also give their Hodge number and syzygies.
