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arXiv · 1209.5618

Foliations by Curves with Curves as Singularities

Maurício Corrêa Jr·Arturo Fernandez Perez·Gilcione Nonato Costa·Renato Vidal Martins
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Abstract

Let $\mathcal F$ be a holomorphic one-dimensional foliation on $\mathbb{P}^n$ such that the components of its singular locus $Σ$ are curves $C_i$ and points $p_j$. We determine the number of $p_j$, counted with multiplicities, in terms of invariants of $\mathcal F$ and $C_i$, assuming that $\mathcal F$ is special along the $C_i$. Allowing just one nonzero dimensional component on $Σ$, we also prove results on when the foliation happens to be determined by its singular locus.

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Maurício Corrêa Jr, Arturo Fernandez Perez, Gilcione Nonato Costa, Renato Vidal Martins. 2012-09-25. Foliations by Curves with Curves as Singularities. https://doi.org/10.5802/aif.2896

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