论文标题
复曲叶叶的理性回调
Rational pullbacks of toric foliations
论文作者
论文摘要
本文致力于研究单数编码的研究$ 1 $ foliations $ \ MATHCAL {f} $上的简单完整的圆磨品种$ x $及其回调，由主导理性地图$φ：\ Mathbb {p}^n \ dashrightArrow x $。首先，我们描述了$ \ MATHCAL {F} $的奇异性和$φ^*\ Mathcal {f} $的$（φ，\ Mathcal {f}）$。然后，我们表明，$φ^*\ MATHCAL {f} $的一阶变形是由一阶展开产生的是$ $φ__\ VAREPSILON^*\ MATHCAL {f} $的家族，其中$φ__\ VAREPSILON $是$φ$的扰动。我们还证明，$φ^*\ Mathcal {f} _ \ varepsilon $的形式的变形完全由与$φ$的纤维相切的家族组成。为了做到这一点，我们陈述了有关这些叶子的库普卡奇异性的一些独立兴趣的结果。
This article is dedicated to the study of singular codimension $1$ foliations $\mathcal{F}$ on a simplicial complete toric variety $X$ and their pullbacks by dominant rational maps $φ:\mathbb{P}^n\dashrightarrow X$. First, we describe the singularities of $\mathcal{F}$ and $φ^*\mathcal{F}$ for a generic pair $(φ,\mathcal{F})$. Then we show that the first order deformations of $φ^*\mathcal{F}$ arising from first order unfoldings are the families of the form $φ_\varepsilon^*\mathcal{F}$, where $φ_\varepsilon$ is a perturbation of $φ$. We also prove that the deformations of the form $φ^*\mathcal{F}_\varepsilon$ consist exactly of the families which are tangent to the fibers of $φ$. In order to do so, we state some results of independent interest regarding the Kupka singularities of these foliations.
