19 citations · 78 across the 19 of their papers we have counts for
20 papers
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…
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…
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…
A short proof of the classification of higher rank invariant subvarieties in genus three
Paul Apisa
We give a new short proof of the classification of rank at least two invariant subvarieties in genus three, which is due to Aulicino, Nguyen, and Wright. The proof uses techniques…
Algebraically primitive invariant subvarieties with quadratic field of definition
Paul Apisa, David Aulicino
We show that the only algebraically primitive invariant subvarieties of strata of translation surfaces with quadratic field of definition are the decagon, Weierstrass curves, and e…
Moduli spaces of complex affine and dilation surfaces
Paul Apisa, Matt Bainbridge, Jane Wang
We construct moduli spaces of complex affine and dilation surfaces. Using ideas of Veech, we show that the the moduli space of affine surfaces with fixed genus and with cone points…