Abstract
We investigate a construction providing pairs of Calabi-Yau varieties described as zero loci of pushforwards of a hyperplane section on a roof as described by Kanemitsu. We discuss the implications of such construction at the level of Hodge equivalence, derived equivalence and mathbb L-equivalence. For the case of K3 surfaces, we provide alternative interpretations for the Fourier-<PRE_TAG>Mukai duality</POST_TAG> in the family of K3 surfaces of degree 12 of Mukai. In all these constructions the derived equivalence lifts to an equivalence of matrix factorizations categories.
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