Pencils on coverings of a given curve whose degree is larger than the Castelnuovo-Severi lower bound
by E. Ballico   C. Keem   D. Shin  

Vol. 2 No. 1 (2007) P.103~P.107

ABSTRACT

Fix integers $q, g, k, d$. Set $\pi_{d,k,q} := kd - d - k + kq + 1$ and assume $q>0,\ k \ge 2,\ d \ge 3q + 1,\ g \ge kq - k + 1$ and $\pi_{d,k,q} - ((\lfloor d/2 \rfloor + 1 - q) \cdot (\lfloor k/2 \rfloor + 1) \le g \le \pi_{d,k,q}$.
Let $Y$ be a smooth and connected genus $q$ projective curve. Here we prove the existence of a smooth and connected genus $g$ projective curve $X$, a degree $k$ morphism $f: X \to Y$ and a degree $d$ morphism $u: X \to P^1$ such that the morphism $(f, u): X \to Y \times P^1$ is birational onto its image.

KEYWORDS
Covering of curves, Brill-Noether theory, ruled surface

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 14H51, 14H30

MILESTONES

Received: 2006-02-20
Revised : 2006-03-31
Accepted:

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