Analytic order of singular and critical points
| dc.creator | Shustin, Eugenii | |
| dc.date | 2002-09-04 | |
| dc.date.accessioned | 2026-07-07T04:50:36Z | |
| dc.date.available | 2026-07-07T04:50:36Z | |
| dc.description | We deal with the following closely related problems: (i) For a germ of a reduced plane analytic curve, what is the minimal degree of an algebraic curve with a singular point analytically equivalent (isomorphic) to the given one? (ii) For a germ of a holomorphic function in two variables with an isolated critical point, what is the minimal degree of a polynomial, equivalent to the given function up to a local holomorphic coordinate change? Classically known estimates for such a degree $d$ in these questions are $\sqrtμ+1\le d\le μ+1$, where $μ$ is the Milnor number. Our result in both the problems is $d\le a\sqrtμ$ with an absolute constant $a$. As a corollary, we obtain asymptotically proper sufficient conditions for the existence of algebraic curves with prescribed singularities on smooth algebraic surfaces. | |
| dc.description | 39 pages, Latex2e | |
| dc.identifier | https://arxiv.org/abs/math/0209043 | |
| dc.identifier | http://arxiv.org/abs/math/0209043 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64852 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14F17, 14H20, 58K05 | |
| dc.title | Analytic order of singular and critical points | |
| dc.type | text |