The boundary of the Milnor fiber of Hirzebruch surface singularities
| dc.creator | Michel, F. | |
| dc.creator | Pichon, Anne | |
| dc.creator | Weber, C. | |
| dc.date | 2005-09-20 | |
| dc.date.accessioned | 2026-07-07T06:18:21Z | |
| dc.date.available | 2026-07-07T06:18:21Z | |
| dc.description | We give the first (as far as we know) complete description of the boundary of the Milnor fiber for some non-isolated singular germs of surfaces in ${\bf C}^3$. We study irreducible (i.e. $gcd (m,k,l) = 1$) non-isolated (i.e. $1 \leq k < l$) Hirzebruch hypersurface singularities in ${\bf C}^3$ given by the equation $z^m - x^ky^l = 0$. We show that the boundary $L$ of the Milnor fiber is always a Seifert manifold and we give an explicit description of the Seifert structure. From it, we deduce that : 1) $L$ is never diffeomorphic to the boundary of the normalization. 2) $L$ is a lens space iff $m = 2$ and $k = 1$. 3) When $L$ is not a lens space, it is never orientation preserving diffeomorphic to the boundary of a normal surface singularity. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0509451 | |
| dc.identifier | http://arxiv.org/abs/math/0509451 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/94706 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J17; 32S25; 57M25 | |
| dc.title | The boundary of the Milnor fiber of Hirzebruch surface singularities | |
| dc.type | text |