Uniform Approximation of Abhyankar Valuation Ideals in Smooth Function Fields
| dc.creator | Ein, Lawrence | |
| dc.creator | Lazarsfeld, Robert | |
| dc.creator | Smith, Karen E. | |
| dc.date | 2002-02-28 | |
| dc.date.accessioned | 2026-07-07T04:46:44Z | |
| dc.date.available | 2026-07-07T04:46:44Z | |
| dc.description | In this paper we use the theory of multiplier ideals to show that the valuation ideals of a rank one Abhyankar valuation centered at a smooth point of a complex algebraic variety are approximated, in a quite strong sense, by sequences of powers of fixed ideals. Fix a rank one valuation v centered at a smooth point x on an algebraic variety over a field of characteristic zero. Assume that v is Abhyankar, that is, that its rational rank plus its transcendence degree equal the dimension of the variety. Let a_m denote the ideal of elements in the local ring of x whose valuations are at least m. Our main theorem is that there exists e>0 such that a_{mn} is contained in (a_{m-e})^n for all m and n. This can be viewed as a greatly strengthened form of Izumi's Theorem for Abhyankar valuations centered on smooth complex varieties. | |
| dc.description | 27 pages, latex | |
| dc.identifier | https://arxiv.org/abs/math/0202303 | |
| dc.identifier | http://arxiv.org/abs/math/0202303 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63454 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A18 | |
| dc.title | Uniform Approximation of Abhyankar Valuation Ideals in Smooth Function Fields | |
| dc.type | text |