Gianluca Faraco

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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…

math.GT2018

Geometrization of almost extremal representations in $PSL_{2} R$

Gianluca Faraco

Let $S$ be a closed surface of genus $g$ . In this paper, we investigate the relationship between hyperbolic cone-structure on $S$ and representations of the fundamental group into…

On the symplectic geometry of branched hyperbolic surfaces in genus two

Relative period realization of holomorphic differentials with prescribed invariants

Geometrization of almost extremal representations in PSL2​R

Geometrization of almost extremal representations in $PSL_{2} R$