The mirror dual of the cubic threefold

We construct the mirror dual of the cubic threefold using a duality of Landau Ginzburg models that has been developed in a joint work with Mark Gross and Ludmil Katzarkov for the study of mirror duals of varieties of general type. We show that our five-dimensional model is equivalent to the three-dimensional ones from the literature and study its geometry in detail, verify a conjecture of Katzarkov, discuss the cohomology of the sheaf of vanishing cycles, homological mirror symmetry and Orlov's theorem.