GL2ℝ–invariant measures in marked strata : generic marked points, Earle–Kra for strata and illumination

Apisa, Paul¹

¹ Department of Mathematics, University of Chicago, Chicago, IL, United States, Department of Mathematics, Yale University, New Haven, CT, United States

Geometry & topology, Tome 24 (2020) no. 1, pp. 373-408.

Résumé

We show that nontrivial $GL\left(2,ℝ\right)$–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 Teichmüller disk. We also solve the finite blocking problem for generic translation surfaces.

Détail

DOI : 10.2140/gt.2020.24.373

Classification : 30F60, 32G15, 37F30
Keywords: dynamics on Teichmüller space, flat surfaces, translation surfaces

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