Exemples de surfaces canoniques de ${\mathbb{P}}^6$ et de solides de Calabi-Yau de ${\mathbb{P}}^7$

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.