### Impacto

Gamboa Mutuberria, José Manuel and Bujalance, E. and Etayo Gordejuela, J. Javier
(1987)
*Topological Types Of P-Hyperelliptic Real Algebraic-Curves.*
Mathematische Zeitschrift, 194
(2).
pp. 275-283.
ISSN 0025-5874

Official URL: http://www.springerlink.com/content/w314656u16881r67/

## Abstract

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 order

2, 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.

Item Type: | Article |
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Uncontrolled Keywords: | topological types of p-hyperelliptic real algebraic curves; existence of phyperelliptic real algebraic curves; genus |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 15468 |

Deposited On: | 01 Jun 2012 10:55 |

Last Modified: | 01 Jun 2012 10:55 |

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