Abstract
A pseudo-real Riemann surface admits anticonformal automorphisms but no anticonformal involution. We obtain the classification of actions and groups of automorphisms of pseudo-real Riemann surfaces of genera 2, 3 and 4. For instance the automorphism group of a pseudo-real Riemann surface of genus 4 is either C 4 or C 8 or the Fröbenius group of order 20, and in the case of C 4 there are exactly two possible topological actions. Let M K PR,g be the set of surfaces in the moduli space M K g corresponding to pseudo-real Riemann surfaces. We obtain the equisymmetric stratification of M K PR,g for genera g = 2, 3, 4, and as a consequence we have that M K PR,g is connected for g = 2, 3 but M K PR,4 has three connected components.
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Supported by Spanish Government Research (Grant No. MTM2011-23092)
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Bujalance, E., Costa, A.F. Automorphism groups of pseudo-real Riemann surfaces of low genus. Acta. Math. Sin.-English Ser. 30, 11–22 (2014). https://doi.org/10.1007/s10114-013-2420-9
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DOI: https://doi.org/10.1007/s10114-013-2420-9