Enriched Relative Polar Curves and Discriminants
| dc.creator | Massey, David B. | |
| dc.date | 2006-07-07 | |
| dc.date | 2006-07-26 | |
| dc.date.accessioned | 2026-07-07T07:18:10Z | |
| dc.date.available | 2026-07-07T07:18:10Z | |
| dc.description | Let $(f, g)$ be a pair of complex analytic functions on a singular analytic space $X$. We give ``the correct'' definition of the relative polar curve of $(f, g)$, and we give a very formal generalization of Lê's attaching result, which relates the relative polar curve to the relative cohomology of the Milnor fiber modulo a hyperplane slice. We also give the technical arguments which allow one to work with a derived category version of the discriminant and Cerf diagram of a pair of functions. From this, we derive a number of generalizations of results which are classically proved using the discriminant. In particular, we give applications to families of isolated ``critical points''. | |
| dc.description | 34 pages, the revision contains a new section | |
| dc.identifier | https://arxiv.org/abs/math/0607210 | |
| dc.identifier | http://arxiv.org/abs/math/0607210 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114205 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32B15, 32C35, 32C18, 32B10 | |
| dc.title | Enriched Relative Polar Curves and Discriminants | |
| dc.type | text |