论文标题
Halphen铅笔的明确结构
Explicit Constructions of Halphen Pencils
论文作者
论文摘要
我们通过在射影平面$ \ mathbb {p}^2 $中明确构建其相关的Halphen铅笔来构建索引两的合理椭圆表面。对于发生的每种类型的奇异纤维，我们构建了至少一个具有该类型纤维的示例，实际上，对于某些纤维，我们构建了所有可能的示例。我们在有理椭圆表面和相应的平面曲线中建立了精确的词典，尤其是我们研究了在Halphen铅笔中出现的曲线的奇异性。
We construct rational elliptic surfaces of index two by explicitly constructing their associated Halphen pencils in the projective plane $\mathbb{P}^2$. For each of the types of singular fibers that occur we construct at least one example having that type of fiber and in fact, for some, we construct all possible examples. We establish a precise dictionary between the fibers in a rational elliptic surface and the corresponding plane curves and, in particular, we study the singularities of the curves appearing in a Halphen pencil.
