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ON THE INDEX OF VECTOR FIELDS TANGENT TO HYPERSURFACES WITH NON-ISOLATED SINGULARITIES

2002; Wiley; Volume: 65; Issue: 02 Linguagem: Inglês

10.1112/s0024610701002988

1469-7750

Luis Giraldo, Xavier Gómez-Mont, Pavao Mardešić,

Advanced Differential Equations and Dynamical Systems

Journal of the London Mathematical SocietyVolume 65, Issue 2 p. 418-438 Notes and Papers On the Index of Vector Fields Tangent to Hypersurfaces with Non-Isolated Singularities L. Giraldo, L. Giraldo Departamento de Algebra, Facultad de Matemáticas, Universidad Complutense de Madrid, Ciudad Universitaria, 28040 Madrid, Spain, [email protected]Search for more papers by this authorX. Gómez-Mont, X. Gómez-Mont CIMAT, AP 402, Guanajuato 36000, Mexico, [email protected]Search for more papers by this authorP. Mardešić, P. Mardešić Laboratoire de Topologie, Université de Bourgogne, UMR 5584 du CNRS, BP 44870, 21078-Dijon Cedex, France, [email protected]Search for more papers by this author L. Giraldo, L. Giraldo Departamento de Algebra, Facultad de Matemáticas, Universidad Complutense de Madrid, Ciudad Universitaria, 28040 Madrid, Spain, [email protected]Search for more papers by this authorX. Gómez-Mont, X. Gómez-Mont CIMAT, AP 402, Guanajuato 36000, Mexico, [email protected]Search for more papers by this authorP. Mardešić, P. Mardešić Laboratoire de Topologie, Université de Bourgogne, UMR 5584 du CNRS, BP 44870, 21078-Dijon Cedex, France, [email protected]Search for more papers by this author First published: 23 December 2016 https://doi.org/10.1112/S0024610701002988Citations: 7AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract Let F be a germ of a holomorphic function at 0 in Cn+1, having 0 as a critical point not necessarily isolated, and let X ˜ : = ∑ j = 0 n X j ( ∂ / ∂ z j ) be a germ of a holomorphic vector field at 0 in Cn+1 with an isolated zero at 0, and tangent to V := F−1(0). Consider the OV,0-complex obtained by contracting the germs of Kähler differential forms of V at 0 Ω V , 0 i : = Ω C n + 1 , 0 i F Ω C n + 1 , 0 i + d F ∧ Ω C n + 1 , 0 i − 1 (0.1) with the vector field X:= X ˜ |V on V: 0 ← O ← V , 0 ← X Ω V , 0 1 ← X … ← X Ω V , 0 n ← X Ω V , 0 n + 1 ← 0. (0.2) Citing Literature Volume65, Issue2April 2002Pages 418-438 RelatedInformation