کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4597228 | 1336206 | 2010 | 9 صفحه PDF | دانلود رایگان |

Our knowledge of linear series on real algebraic curves is still very incomplete. In this paper we restrict to pencils (complete linear series of dimension one). Let XX denote a real curve of genus gg with real points and let k(R)k(R) be the smallest degree of a pencil on XX (the real gonality of XX). Then we can find on XX a base point free pencil of degree g+1g+1 (resp. gg if XX is not hyperelliptic, i.e. if k(R)>2k(R)>2) with an assigned geometric behaviour w.r.t. the real components of XX, and if g=2n−2(n≥1) we prove that k(R)≤g2+1 which is the same bound as for the gonality of a complex curve of even genus gg. Furthermore, if the complexification of XX is a kk-gonal curve (k≥2)(k≥2) one knows that k≤k(R)≤2k−2k≤k(R)≤2k−2, and we show that for any two integers k≥2k≥2 and 0≤n≤k−20≤n≤k−2 there is a real curve with real points and kk-gonal complexification such that its real gonality is k+nk+n.
Journal: Journal of Pure and Applied Algebra - Volume 214, Issue 6, June 2010, Pages 841–849