Hyperelliptic translation surfaces and folded tori

摘要

Following constructions of McMullen and Vasilyev we list strict quadratic differentials on (marked) tori defined by twists of one-forms on hyperelliptic surfaces. We count the total number of twists in each genus and show that the quadratic differentials on (marked) tori are strict. Taking universal covers we obtain a variety of (non-arithmetic) lattice Panov planes from genus two lattice surfaces.