3 papers
math.AG2026
Components of strata of k-differentials and their orbit closures
Paul Apisa, Juliet Aygun
We obtain a complete classification of components of strata of holomorphic and meromorphic k-differentials. We show that, when genus is at least two and outside of explicit excepti…
math.AG2025
Holonomy of affine surfaces
Paul Apisa, Matt Bainbridge, Jane Wang
We identify the moduli space of complex affine surfaces with the moduli space of regular meromorphic connections on Riemann surfaces and show that it satisfies a corresponding univ…
math.GT2025
Invariant measures on moduli spaces of twisted holomorphic 1-forms and strata of dilation surfaces
Paul Apisa, Nick Salter
The moduli space of twisted holomorphic 1-forms on Riemann surfaces, equivalently dilation surfaces with scaling, admits a stratification and GL(2,R)-action as in the case of modul…