Halphen Pencils on Weighted Fano Threefold Hypersurfaces

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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

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