On the automorphism groups of certain branched structures on surfaces

Gianluca Faraco

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arXiv · 2207.12861

On the automorphism groups of certain branched structures on surfaces

Gianluca Faraco

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Abstract

We consider translation surfaces with poles on surfaces. We shall prove that any finite group appears as the automorphism group of some translation surface with poles. As a direct consequence we obtain the existence of structures achieving the maximal possible number of automorphisms allowed by their genus and we finally extend the same results to branched projective structures.

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Gianluca Faraco. 2022-07-26. On the automorphism groups of certain branched structures on surfaces. https://arxiv.org/abs/2207.12861

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