Marked points on translation surfaces

TL;DR

This paper classifies all GL(2,R) equivariant point markings on translation surfaces, showing they originate from branched coverings and periodic points, and applies this to the finite blocking problem.

Contribution

It provides a complete classification of point markings over strata of quadratic differentials and links them to branched coverings and periodic points.

Findings

All GL(2,R) equivariant point markings are from branched coverings and periodic points.

Complete classification over strata of quadratic differentials.

Applications to the finite blocking problem.

Abstract

We show that all GL(2,R) equivariant point markings over orbit closures of translation surfaces arise from branched covering constructions and periodic points, completely classify such point markings over strata of quadratic differentials, and give applications to the finite blocking problem.