Superheavy Skeleta for non-Normal Crossings Divisors

Given an anticanonical divisor in a projective variety, one naturally obtains a monotone K\"ahler manifold. In this paper, for divisors in a certain class (larger than normal crossings), we construct smoothing families of contact hypersurfaces with controlled Reeb dynamics. We use these to adapt arguments of Borman, Sheridan and Varolgunes to obtain analogous results about symplectic cohomology with supports in the divisor complement. In particular, we will show that several examples of Lagrangian skeleta of such divisor complements are superheavy, in cases where applying Lagrangian Floer theory may be intractable.