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- W3023751589 abstract "A Riemann surface [Formula: see text] having field of moduli ℝ, but not a field of definition, is called pseudo-real. This means that [Formula: see text] has anticonformal automorphisms, but none of them is an involution. A Riemann surface is said to be plane if it can be described by a smooth plane model of some degree d ≥ 4 in [Formula: see text]. We characterize pseudo-real-plane Riemann surfaces [Formula: see text], whose conformal automorphism group Aut + ([Formula: see text]) is PGL 3 (ℂ)-conjugate to a finite non-trivial group that leaves invariant infinitely many points of [Formula: see text]. In particular, we show that such pseudo-real-plane Riemann surfaces exist only if Aut + ([Formula: see text]) is cyclic of even order n dividing the degree d. Explicit families of pseudo-real-plane Riemann surfaces are given for any degree d = 2pm with m > 1 odd, p prime and n = d/p." @default.
- W3023751589 created "2020-05-13" @default.
- W3023751589 creator A5059041901 @default.
- W3023751589 date "2020-05-07" @default.
- W3023751589 modified "2023-10-16" @default.
- W3023751589 title "A Class of Pseudo-Real Riemann Surfaces with Diagonal Automorphism Group" @default.
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- W3023751589 doi "https://doi.org/10.1142/s1005386720000206" @default.
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