A note on M. Soares’ bounds

Eduardo Esteves[1]; Israel Vainsencher[2]

  • [1] IMPA Estrada D. Castorina 110 Jardim Botânico 22460-320 Rio de Janeiro RJ (Brasil)
  • [2] UFMG Departamento de Matemática Cidade Universitária 30123-970 Belo Horizonte  MG (Brasil)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 1, page 269-276
  • ISSN: 0373-0956

Abstract

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We give an intersection theoretic proof of M. Soares’ bounds for the Poincaré-Hopf index of an isolated singularity of a foliation of ℂℙ n .

How to cite

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Esteves, Eduardo, and Vainsencher, Israel. "A note on M. Soares’ bounds." Annales de l’institut Fourier 56.1 (2006): 269-276. <http://eudml.org/doc/10142>.

@article{Esteves2006,
abstract = {We give an intersection theoretic proof of M. Soares’ bounds for the Poincaré-Hopf index of an isolated singularity of a foliation of $\mathbb\{CP\}^ n$.},
affiliation = {IMPA Estrada D. Castorina 110 Jardim Botânico 22460-320 Rio de Janeiro RJ (Brasil); UFMG Departamento de Matemática Cidade Universitária 30123-970 Belo Horizonte  MG (Brasil)},
author = {Esteves, Eduardo, Vainsencher, Israel},
journal = {Annales de l’institut Fourier},
keywords = {intersection theory; singularities; foliations},
language = {eng},
number = {1},
pages = {269-276},
publisher = {Association des Annales de l’institut Fourier},
title = {A note on M. Soares’ bounds},
url = {http://eudml.org/doc/10142},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Esteves, Eduardo
AU - Vainsencher, Israel
TI - A note on M. Soares’ bounds
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 1
SP - 269
EP - 276
AB - We give an intersection theoretic proof of M. Soares’ bounds for the Poincaré-Hopf index of an isolated singularity of a foliation of $\mathbb{CP}^ n$.
LA - eng
KW - intersection theory; singularities; foliations
UR - http://eudml.org/doc/10142
ER -

References

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  1. E. Esteves, The Castelnuovo-Mumford regularity of an integral variety of a vector field on projective space, Math. Res. Lett. 9 (2002), 1-15 Zbl1037.14022MR1892310
  2. W. Fulton, Intersection theory, (1985), Springer, New York Zbl0541.14005MR732620
  3. P. Griffiths, J. Harris, Principles of algebraic geometry, (1978), John Wiley & Sons, New York Zbl0408.14001MR507725
  4. M. Soares, The Poincaré problem for hypersurfaces invariant by one-dimensional foliations, Invent. math. 128 (1997), 495-500 Zbl0923.32025MR1452431
  5. M. Soares, Bounding Poincaré-Hopf indices and Milnor numbers, Math. Nachrichten 278 (2005), 703-711 Zbl1069.32014MR2135502
  6. T. Suwa, Indices of vector fields and residues of singular holomorphic foliations, (1998), Hermann, Paris Zbl0910.32035MR1649358
  7. I. Vainsencher, Classes características em geometria algébrica, (1985), IMPA, Rio de Janeiro MR812276

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