Shinya Kitagawa (NIT, Gifu College)

Examples of genus two fibrations without sections on rational surfaces

Abstract

Let S be a smooth complex projective rational surface equipped with a relatively minimal fibration f of genus two. It is known that the second Betti number b_2 of S can be 11, 12, 13 or 14. If b_2 is 13 or 14, then f always admits a section. In Proc. Japan Acard., 93, Ser. A (2017), I constructed an explicit example of S such that b_2=12, the fibres of f contain at least one irreducible component which is reduced, and f admits no sections. In this talk, I will introduce such examples of b_2=11.