## Tsukuba Journal of Mathematics

### On triple coverings of irrational curves

#### Abstract

Given a triple covering $X$ of genus $g$ of a general (in the sense of Brill-Noether) curve $C$ of genus $h$, we show the existence of base-point-free pencils of degree $d$ which are not composed with the triple covering for any $d\geq g-[(3h+1)/2]-1$ by utilizing some enumerative methods and computations. We also discuss about the sharpness of our main result and the so-called Castelnuovo-Severi bound by exhibiting some examples.

#### Article information

Source
Tsukuba J. Math., Volume 21, Number 2 (1997), 421-441.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496163250

Digital Object Identifier
doi:10.21099/tkbjm/1496163250

Mathematical Reviews number (MathSciNet)
MR1473931

Zentralblatt MATH identifier
0908.14009

#### Citation

Kato, Takao; Keem, Changho; Ohbuchi, Akira. On triple coverings of irrational curves. Tsukuba J. Math. 21 (1997), no. 2, 421--441. doi:10.21099/tkbjm/1496163250. https://projecteuclid.org/euclid.tkbjm/1496163250