Relative linear extensions of sextic del Pezzo fibrations over curves

Abstract

In this paper, we study a sextic del Pezzo fibration over a curve comprehensively. We obtain certain formulae of several basic invariants of such a fibration. We also establish the embedding theorem of such a fibration which asserts that every such a fibration is a relative linear section of a Mori fiber space with the general fiber (P 1 ) 3 and that with the general fiber (P 2 ) 2 . As an application of this embedding theorem, we classify singular fibers of such a fibrations and answer a question of T. Fujita about existence of non-normal fibers.