A cascade of determinantal Calabi--Yau threefolds
  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. 
Grzegorz Kapustka, Michal Kapustka