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Eduardo Esteves; Israel Vainsencher
A note on M. Soares’ bounds
(Une note sur les bornes de M. Soares)
Annales de l'institut Fourier, 56 no. 1 (2006), p. 269-276, doi: 10.5802/aif.2180
Article PDF | Reviews MR 2228688 | Zbl 1089.32025
Class. Math.: 32S65, 14C17, 37F75
Keywords: intersection theory, singularities, foliations
[1] E. Esteves, “The Castelnuovo-Mumford regularity of an integral variety of a vector field on projective space”, Math. Res. Lett. 9 (2002), p. 1-15 MR 1892310 | Zbl 1037.14022
[2] W. Fulton, Intersection theory, Springer, New York, 1985 MR 732620 | Zbl 0541.14005
[3] P. Griffiths & J. Harris, Principles of algebraic geometry, John Wiley & Sons, New York, 1978 MR 507725 | Zbl 0408.14001
[4] M. Soares, “The Poincaré problem for hypersurfaces invariant by one-dimensional foliations”, Invent. math. 128 (1997), p. 495-500 Article | MR 1452431 | Zbl 0923.32025
[5] M. Soares, “Bounding Poincaré-Hopf indices and Milnor numbers”, Math. Nachrichten 278 (2005) no. 6, p. 703-711 Article | MR 2135502 | Zbl 02183902
[6] T. Suwa, Indices of vector fields and residues of singular holomorphic foliations, Hermann, Paris, 1998 MR 1649358 | Zbl 0910.32035
[7] I. Vainsencher, Classes características em geometria algébrica, IMPA, Rio de Janeiro, 1985 MR 812276
Eduardo Esteves; Israel Vainsencher
A note on M. Soares’ bounds
(Une note sur les bornes de M. Soares)
Annales de l'institut Fourier, 56 no. 1 (2006), p. 269-276, doi: 10.5802/aif.2180
Article PDF | Reviews MR 2228688 | Zbl 1089.32025
Class. Math.: 32S65, 14C17, 37F75
Keywords: intersection theory, singularities, foliations
Résumé - Abstract
We give an intersection theoretic proof of M. Soares’ bounds for the Poincaré-Hopf index of an isolated singularity of a foliation of $\mathbb{CP}^ n$.
Bibliography
[2] W. Fulton, Intersection theory, Springer, New York, 1985 MR 732620 | Zbl 0541.14005
[3] P. Griffiths & J. Harris, Principles of algebraic geometry, John Wiley & Sons, New York, 1978 MR 507725 | Zbl 0408.14001
[4] M. Soares, “The Poincaré problem for hypersurfaces invariant by one-dimensional foliations”, Invent. math. 128 (1997), p. 495-500 Article | MR 1452431 | Zbl 0923.32025
[5] M. Soares, “Bounding Poincaré-Hopf indices and Milnor numbers”, Math. Nachrichten 278 (2005) no. 6, p. 703-711 Article | MR 2135502 | Zbl 02183902
[6] T. Suwa, Indices of vector fields and residues of singular holomorphic foliations, Hermann, Paris, 1998 MR 1649358 | Zbl 0910.32035
[7] I. Vainsencher, Classes características em geometria algébrica, IMPA, Rio de Janeiro, 1985 MR 812276
© Annales de L'Institut Fourier - ISSN (électronique) : 1777-5310