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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.

##### MSC:
 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
##### Keywords:
Kulkarni surface; compact Riemann surface
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