The full automorphism group of the Kulkarni surface. (English) Zbl 0892.30033

Turbek, Peter

Rev. Mat. Univ. Complutense Madr. 10, No. 2, 265-276 (1997).

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.

Reviewer: C.Maclachlan (Aberdeen)

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