Real and complex indices of vector fields on complete intersection curves with isolated singularity
| dc.creator | Klehn, Oliver | |
| dc.date | 2003-01-15 | |
| dc.date | 2004-02-04 | |
| dc.date.accessioned | 2026-07-07T04:54:28Z | |
| dc.date.available | 2026-07-07T04:54:28Z | |
| dc.description | If (V,0) is an isolated complete intersection singularity and X a holomorphic vector field tangent to V one can define an index of X, the so called GSV index, which generalizes the Poincare-Hopf index. We prove that the GSV index coincides with the dimension of a certain explicitely constructed vector space, if X is deformable in a certain sense and V is a curve. We also give a sufficient algebraic criterion for X to be deformable in this way. If one considers the real analytic case one can also define an index of X which is called the real GSV index. Under the condition that X has the deformation property, we prove a signature formula for the index generalizing the Eisenbud-Levine Theorem. | |
| dc.description | Major revision. Main changes are the corrections of the statements and proofs of the main theorems. 16 pages, to appear in Compositio Mathematica | |
| dc.identifier | https://arxiv.org/abs/math/0301166 | |
| dc.identifier | http://arxiv.org/abs/math/0301166 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66266 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32S65 (Primary); 14B05, 13H10 (Secondary) | |
| dc.title | Real and complex indices of vector fields on complete intersection curves with isolated singularity | |
| dc.type | text |