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The full automorphism group of the Kulkarni surface. (English) Zbl 0892.30033
For each \(g\equiv 3 \pmod 4\), the Kulkarni surface is a compact Riemann surface of genus \(g\) which admits an automorphism group of order \(8g+8\). This surface has defining equation \[ z^{2g+2}- (x-1) x^{g-1} (x+1)^{g+2} =0. \] The author explicitly describes the generators of the automorphism group as transformations of \(x,z\). The surface also admits three conjugacy classes of anti-conformal involutions with fixed points and with respect to each of these, a defining equation is given which exhibits these symmetries as complex conjugation.

30F10 Compact Riemann surfaces and uniformization
30F50 Klein surfaces
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
14H55 Riemann surfaces; Weierstrass points; gap sequences
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