Perverse schobers and Orlov equivalences

A perverse schober is a categorification of a perverse sheaf proposed by Kapranov–Schechtman. In this paper, we construct examples of perverse schobers on the Riemann sphere, which categorify the intersection complexes of natural local systems arising from the mirror symmetry for Calabi-Yau hypersurfaces. The Orlov equivalence plays a key role for the construction.