Mukai duality via roofs of projective bundles

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 in Kanemitsu (Preprint, arXiv:1812.05392, 2018). We discuss the implications of such construction at the level of Hodge equivalence, derived equivalence and L ${\mathbb {L}}$ -equivalence. For the case of K3 surfaces, we provide alternative interpretations for the Fourier–Mukai duality in the family of K3 surfaces of degree 12 of (New trends in algebraic geometry (Warwick, 1996), Lond. Math. Soc. Lecture Note Ser., vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 311–326). In all these constructions, the derived equivalence lifts to an equivalence of matrix factorizations categories.