论文标题
在内姆布鲁克表面上具有孤立奇异性的叶子
Foliations with isolated singularities on Hirzebruch surfaces
论文作者
论文摘要
我们研究Hirzebruch表面上的叶子$ \ MATHCAL {F} $ $S_δ$，并证明，与投影平面上的叶面相似，任何$ \ MATHCAL {F} $都可以由Bi-Bosomeenos的多项式封闭式$ 1 $ -Form-form代表。如果$ \ MATHCAL {F} $具有孤立的奇异性，我们表明，对于$δ= 1 $，$ \ Mathcal {f} $的奇异方案确实决定了叶面，除了一些例外，我们描述的是投射平面中的叶子的情况。对于$δ\ neq 1 $，我们证明$ \ mathcal {f} $的单数方案不能确定叶面。但是，我们证明，在大多数情况下，两种叶子$ \ mathcal {f} $和$ \ Mathcal {f}'$由$ s $和$ s'$给出的$ s'=φ（s）$具有相同的单数方案，但对于某些全球endolphist $ s'=φ（s）$。
We study foliations $\mathcal{F}$ on Hirzebruch surfaces $S_δ$ and prove that, similarly to those on the projective plane, any $\mathcal{F}$ can be represented by a bi-homogeneous polynomial affine $1$-form. In case $\mathcal{F}$ has isolated singularities, we show that, for $ δ=1 $, the singular scheme of $\mathcal{F}$ does determine the foliation, with some exceptions that we describe, as is the case of foliations in the projective plane. For $δ\neq 1$, we prove that the singular scheme of $\mathcal{F}$ does not determine the foliation. However we prove that, in most cases, two foliations $\mathcal{F}$ and $\mathcal{F}'$ given by sections $s$ and $s'$ have the same singular scheme if and only if $s'=Φ(s)$, for some global endomorphism $Φ$ of the tangent bundle of $S_δ$.
