2024/01/09 by Benjamin Dozier, Dozier, Benjamin
Mathematics · #Algebraic and Geometric Analysis #Holomorphic and Operator Theory #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2401.04844
In this informal expository note, we quickly introduce and survey compactifications of strata of holomorphic 1-forms on Riemann surfaces, i.e. spaces of translation surfaces. In the last decade, several of these have been constructed, studied, and successfully applied to problems. We discuss relations between their definitions and properties, focusing on the different notions of convergence from a flat geometric perspective.