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math.GT2025
On the symplectic geometry of branched hyperbolic surfaces in genus two
Gianluca Faraco, Arnaud Maret
We construct analogues of Fenchel-Nielsen coordinates on an open and dense subset of the space of holonomies of branched hyperbolic structures on a closed genus-2 surface. We show…
math.GT2025
Relative period realization of holomorphic differentials with prescribed invariants
Dawei Chen, Gianluca Faraco
We provide a complete description of realizable relative period representations for holomorphic differentials on Riemann surfaces with prescribed orders of zeros and additional inv…