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.

arXiv comment32 pages, no figures. Final version based on the referee report. To appear in Veech special volume of Journal of Modern Dynamics