论文标题
仿射线在具有不可还原边界的理性仿射表面上进行的振动
Fibrations by affine lines on rational affine surfaces with irreducible boundaries
论文作者
论文摘要
我们将仿射线的振动视为平滑仿射表面上的平滑仿射表面的补充，$ b $在光滑的投影表面上$ x $定义在特征零的代数闭合场上。我们观察到，除两个例外外，这些表面$ x \ setminus b $允许许多$ \ mathbb {a}^1 $ - 纤维纤维上的$ \ mathbb {a}^1 $ - 纤维纤维的纤维纤维和独特的独特奇特纤维的任意大量多样性。对于$ \ mathbb {a}^1 $ - 纤维线上的纤维纤维，我们给出一个新的且本质上具有独立的证据，证明了这种纤维化的等效类别的集合，即在源和目标上由$ x $ by by by by bely x $ bely或2lose coples the source and Targets在源和目标上的组成是有限的。
We consider fibrations by affine lines on smooth affine surfaces obtained as complements of smooth rational curves $B$ in smooth projective surfaces $X$ defined over an algebraically closed field of characteristic zero. We observe that except for two exceptions, these surfaces $X \setminus B$ admit infinitely many families of $\mathbb{A}^1$-fibrations over the projective line with irreducible fibers and a unique singular fiber of arbitrarily large multiplicity. For $\mathbb{A}^1$-fibrations over the affine line, we give a new and essentially self-contained proof that the set of equivalence classes of such fibrations up to composition by automorphisms at the source and target is finite if and only if the self-intersection number of $B$ in $X$ is less than or equal to 6.
