The Kontsevich–Zorich cocycle over Veech–Mcmullen family of symmetric translation surfaces

Abstract

We describe the Kontsevich-Zorich cocycle over an affine invariant orbifold coming from a (cyclic) covering construction inspired by works of Veech and McMullen. In particular, using the terminology in a recent paper of Filip, we show that all cases of Kontsevich-Zorich monodromies of SU(p,q) type are realized by appropriate covering constructions.