Hirotaka Ishida (Tohoku Gakuin University)

On certain triple coverings of projective line bundles

Abstract

There exists a lower bound for the relative Euler-Poincaré characteristic of fibrations which are constructed by cyclic triple coverings of ruled surfaces. However, the existence of such fibration is not clear because the above lower bound is obtained by numerical arguments. In this talk, we construct explicitly cyclic triple coverings, and prove the existence of trigonal fibrations with slope 24/5 and sufficiently large relative Euler-Poincaré characteristic.