%0 Journal Article
%A Bujalance García, Emilio
%A Etayo Gordejuela, José Javier
%A Gamboa Mutuberria, José Manuel
%T Topological Types Of P-Hyperelliptic Real Algebraic-Curves
%D 1987
%@ 0025-5874
%U https://hdl.handle.net/20.500.14352/64629
%X Given a natural number p, a projective irreducible smooth algebraic curve V defined over R is called p-hyperelliptic if there exists a birational isomorphism of V, of order2, such that V/ has genus p. This work is concerned with the existence of such curves according to their genus g and the number k of connected components of V(R). We prove that Harnack’s condition 1  k  g is sufficient if V \ V (R) is connected. In case V \ V (R) non-connected, the following conditions 1  k  g + 1 (g + k  1(2)), and either k = g + 1 − 2q for some q, 0 q  p, or  k  2p + 2 with  = 1 for even p, = 2 for odd p, are necessary and sufficient for the existence of the curve.
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