Hypersurface Singularities and Milnor Equisingularity
| dc.creator | Tráng, Lê Dũng | |
| dc.creator | Massey, David B. | |
| dc.date | 2005-04-19 | |
| dc.date.accessioned | 2026-07-07T05:19:14Z | |
| dc.date.available | 2026-07-07T05:19:14Z | |
| dc.description | Suppose that $f$ defines a singular, complex affine hypersurface. If the critical locus of $f$ is one-dimensional at the origin, we obtain new general bounds on the ranks of the homology groups of the Milnor fiber, $F_{f, \mathbf 0}$, of $f$ at the origin, with either integral or $\mathbb Z/p\mathbb Z$ coefficients. If the critical locus of $f$ has arbitrary dimension, we show that the smallest possibly non-zero reduced Betti number of $F_{f, \mathbf 0}$ completely determines if $f$ defines a family of isolated singularities, over a smooth base, with constant Milnor number. This result has a nice interpretation in terms of the structure of the vanishing cycles as an object in the perverse category. | |
| dc.description | A substantial improvement on our earlier paper, Hypersurface Singularities and the Swing. 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0504380 | |
| dc.identifier | http://arxiv.org/abs/math/0504380 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74944 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32B15, 32C35, 32C18, 32B10 | |
| dc.title | Hypersurface Singularities and Milnor Equisingularity | |
| dc.type | text |