Gamboa, J. M. 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/
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.
|Uncontrolled Keywords:||topological types of p-hyperelliptic real algebraic curves; existence of phyperelliptic real algebraic curves; genus|
|Subjects:||Sciences > Mathematics > Algebraic geometry|
|Deposited On:||01 Jun 2012 10:55|
|Last Modified:||02 Mar 2016 15:24|
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