Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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G. Faraco - L. Ruffoni

Complex projective structures with maximal number of Möbius transformations

created by ruffoni on 21 Dec 2019


Published Paper

Inserted: 21 dec 2019
Last Updated: 21 dec 2019

Journal: Mathematische Nachrichten
Year: 2018
Doi: 10.1002/mana.201700371

ArXiv: 1705.06518 PDF


We consider complex projective structures on Riemann surfaces and their groups of projective automorphisms. We show that the structures achieving the maximal possible number of projective automorphisms allowed by their genus are precisely the Fuchsian uniformizations of Hurwitz surfaces by hyperbolic metrics. More generally we show that Galois Bely\u{\i} curves are precisely those Riemann surfaces for which the Fuchsian uniformization is the unique complex projective structure invariant under the full group of biholomorphisms.

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