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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…
math.GT2022
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…