105 citations · 249 across the 12 of their papers we have counts for
12 papers
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…
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…
Haupt's theorem for strata of abelian differentials
Matt Bainbridge, Chris Johnson, Chris Judge +1
Let S be a closed topological surface. Haupt's theorem provides necessary and sufficient conditions for a complex-valued character of the first integer homology group of S to be re…
The moduli space of multi-scale differentials
Matt Bainbridge, Dawei Chen, Quentin Gendron +2
We construct a compactification of the moduli spaces of abelian differentials on Riemann surfaces with prescribed zeroes and poles. This compactification, called the moduli space o…
Strata of -differentials
Matt Bainbridge, Dawei Chen, Quentin Gendron +2
A -differential on a Riemann surface is a section of the -th power of the canonical line bundle. Loci of -differentials with prescribed number and multiplicities of zeros…
Compactification of strata of abelian differentials
Matt Bainbridge, Dawei Chen, Quentin Gendron +2
We describe the closure of the strata of abelian differentials with prescribed type of zeros and poles, in the projectivized Hodge bundle over the Deligne-Mumford moduli space of s…