The space of holomorphic foliations of codimension one and degree $$d\ge 2$$ d ≥ 2 in $${\mathbb {P}}^{n}$$ P n ( $$n\ge 3$$ n ≥ 3 ) has an irreducible component whose general element can be written as a pullback $$F^*{{\mathcal {F}}}$$ F ∗ F , where $${{\mathcal {F}}}$$ F is a general foliation of degree d in $${\mathbb {P}}^{2}$$ P 2 and $$F:{\mathbb {P}}^{n}\dashrightarrow {\mathbb {P}}^{2}$$ F : P n ⤏ P 2 is a general rational linear map. We give a polynomial formula for the degrees of such components.

中文翻译：

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Codimension One 叶面空间的线性回拉分量

$${\mathbb {P}}^{n}$$P n ( $$n\ge 3$$ n ≥ 2 3 ) 有一个不可约分量，其一般元素可以写成一个回调 $$F^*{{\mathcal {F}}}$$ F ∗ F ，其中 $${{\mathcal {F}}}$$ F是 $${\mathbb {P}}^{2}$$ P 2 和 $$F:{\mathbb {P}}^{n}\dashrightarrow {\mathbb {P}} ^{2}$$ F : P n ⤏ P 2 是一般有理线性映射。我们给出了这些分量的度数的多项式公式。