Halphen Pencils on Weighted Fano Threefold Hypersurfaces

Abstract

We classify all pencils on a general weighted hypersurface in $\mathbb{P}(1,a_1,a_2,a_3,a_4)$ of degree ${\sum }_{i=1}^4{a}_i$ whose general members are surfaces of Kodaira dimension zero.

141 pages