%0 Journal Article %T A cascade of determinantal Calabi--Yau threefolds %A Grzegorz Kapustka %A Michal Kapustka %J Mathematics %D 2008 %I arXiv %X We study Kustin--Miller unprojections of Calabi--Yau threefolds. As an application we work out the geometric properties of Calabi--Yau threefolds defined as linear sections of determinantal varieties. We compute their Hodge numbers and describe the morphisms corresponding to the faces of their K\"{a}hler--Mori cone. %U http://arxiv.org/abs/0802.3669v3