Equisingularity and The Euler Characteristic of a Milnor Fibre
| dc.creator | Houston, Kevin | |
| dc.date | 2008-07-03 | |
| dc.date.accessioned | 2026-07-07T09:48:15Z | |
| dc.date.available | 2026-07-07T09:48:15Z | |
| dc.description | We study the Euler characteristic of the Milnor fibre of a hypersurface singularity. This invariant is given in terms of the Euler characteristic of a fibre in between the original singularity and its Milnor fibre and in terms of the Euler characteristics associated to strata of the in-between fibre. From this we can deduce a result of Massey and Siersma regarding singularities with a one-dimensional critical locus. The result is also applied to the study of equisingularity. The famous Briançon-Speder-Teissier result states that a family of isolated hypersurface singularities is equisingular if and only if its $μ^*$-sequence is constant. We show that if a similar sequence for a family of corank 1 complex analytic mappings from n-space to (n+1)-space is constant, then the image of the family of mappings is equisingular. For families of corank 1 maps from 3-space to 4-space we show that the converse is true also. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/0807.0574 | |
| dc.identifier | http://arxiv.org/abs/0807.0574 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164145 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 14B07, 32S55, 32S15, 32S30 | |
| dc.title | Equisingularity and The Euler Characteristic of a Milnor Fibre | |
| dc.type | text |