GL(2)R-invariant measures in marked strata: generic marked points, Earle-Kra for strata and illumination

摘要

We show that nontrivial GL(2, R)-invariant point markings for translation surfaces in strata of abelian differentials exist only when the translation surface belongs to a hyperelliptic component. As an application, we establish constraints on sections of the universal curve restricted to orbifold covers of subvarieties of the moduli space of Riemann surfaces that contain a Teichmuller disk. We also solve the finite blocking problem for generic translation surfaces.