Premium
On the Index of Vector Fields Tangent to Hypersurfaces with Non‐Isolated Singularities
Author(s) -
Giraldo L.,
Gómez-Mont X.,
Mardešić P.
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610701002988
Subject(s) - holomorphic function , vector field , gravitational singularity , field (mathematics) , zero (linguistics) , germ , mathematics , tangent , tangent vector , physics , combinatorics , mathematical analysis , pure mathematics , geometry , linguistics , philosophy
Let F be a germ of a holomorphic function at 0 in C n+1 , having 0 as a critical point not necessarily isolated, and letX ˜ : = ∑ j = 0 nX j( ∂ / ∂ z j)be a germ of a holomorphic vector field at 0 in C n+1 with an isolated zero at 0, and tangent to V := F −1 (0). Consider the O V ,0 ‐complex obtained by contracting the germs of Kähler differential forms of V at 0Ω V , 0 i : =Ω C n + 1 , 0 iF 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)