RT Journal Article
T1 Topological Types Of P-Hyperelliptic Real Algebraic-Curves
A1 Bujalance García, Emilio
A1 Etayo Gordejuela, José Javier
A1 Gamboa Mutuberria, José Manuel
AB 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.
PB Springer
SN 0025-5874
YR 1987
FD 1987
LK https://hdl.handle.net/20.500.14352/64629
UL https://hdl.handle.net/20.500.14352/64629
NO Bujalance García, E., Gamboa Mutuberria, J. M. & Etayo Gordejuela, J. J. «Topological Types Ofp-Hyperelliptic Real Algebraic Curves». Mathematische Zeitschrift, vol. 194, n.o 2, junio de 1987, pp. 275-83. DOI.org (Crossref), https://doi.org/10.1007/BF01161975.
DS Docta Complutense
RD 21 abr 2025