# Foliations by curves with curves as singularities

M. Corrêa Jr^{[1]}; A. Fernández-Pérez^{[1]}; G. Nonato Costa^{[1]}; R. Vidal Martins^{[1]}

- [1] ICEx - UFMG Departamento de Matemática Av. Antônio Carlos 6627 30123-970 Belo Horizonte MG (Brazil)

Annales de l’institut Fourier (2014)

- Volume: 64, Issue: 4, page 1781-1805
- ISSN: 0373-0956

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topCorrêa Jr, M., et al. "Foliations by curves with curves as singularities." Annales de l’institut Fourier 64.4 (2014): 1781-1805. <http://eudml.org/doc/275642>.

@article{CorrêaJr2014,

abstract = {Let $\mathcal\{F\}$ be a holomorphic one-dimensional foliation on $\{\mathbb\{P\}^n\}$ such that the components of its singular locus $\Sigma $ 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 $\Sigma $, we also prove results on when the foliation happens to be determined by its singular locus.},

affiliation = {ICEx - UFMG Departamento de Matemática Av. Antônio Carlos 6627 30123-970 Belo Horizonte MG (Brazil); ICEx - UFMG Departamento de Matemática Av. Antônio Carlos 6627 30123-970 Belo Horizonte MG (Brazil); ICEx - UFMG Departamento de Matemática Av. Antônio Carlos 6627 30123-970 Belo Horizonte MG (Brazil); ICEx - UFMG Departamento de Matemática Av. Antônio Carlos 6627 30123-970 Belo Horizonte MG (Brazil)},

author = {Corrêa Jr, M., Fernández-Pérez, A., Nonato Costa, G., Vidal Martins, R.},

journal = {Annales de l’institut Fourier},

keywords = {holomorphic foliations; non-isolated singularities},

language = {eng},

number = {4},

pages = {1781-1805},

publisher = {Association des Annales de l’institut Fourier},

title = {Foliations by curves with curves as singularities},

url = {http://eudml.org/doc/275642},

volume = {64},

year = {2014},

}

TY - JOUR

AU - Corrêa Jr, M.

AU - Fernández-Pérez, A.

AU - Nonato Costa, G.

AU - Vidal Martins, R.

TI - Foliations by curves with curves as singularities

JO - Annales de l’institut Fourier

PY - 2014

PB - Association des Annales de l’institut Fourier

VL - 64

IS - 4

SP - 1781

EP - 1805

AB - Let $\mathcal{F}$ be a holomorphic one-dimensional foliation on ${\mathbb{P}^n}$ such that the components of its singular locus $\Sigma $ 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 $\Sigma $, we also prove results on when the foliation happens to be determined by its singular locus.

LA - eng

KW - holomorphic foliations; non-isolated singularities

UR - http://eudml.org/doc/275642

ER -

## References

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