Rees algebras and resolution of singularities
| dc.creator | Encinas, Santiago | |
| dc.creator | Villamayor, Orlando | |
| dc.date | 2007-02-27 | |
| dc.date.accessioned | 2026-07-07T09:23:39Z | |
| dc.date.available | 2026-07-07T09:23:39Z | |
| dc.description | Embedded principalization of ideals in smooth schemes, also known as Log-resolutions of ideals, play a central role in algebraic geometry. If two sheaves of ideals, say $I_1$ and $I_2$, over a smooth scheme $V$ have the same integral closure, it is well known that Log-resolution of one of them induces a Log-resolution of the other. On the other hand, in case $V$ is smooth over a field of characteristic zero, an algorithm of desingularization provides, for each sheaf of ideals, a unique Log-resolution. In this paper we show that algorithms of desingularization define the same Log-resolution for two ideals having the same integral closure. We prove this result here by using the form of induction introduced by Włodarczyk. We extend the notion of Log-resolution of ideals over a smooth scheme $V$, to that of Rees algebras over $V$; and then we show that two Rees algebras with the same integral closure undergo the same constructive resolution. The key point is the interplay of integral closure with differential operators. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0702836 | |
| dc.identifier | http://arxiv.org/abs/math/0702836 | |
| dc.identifier | Actas del XVI Coloquio Latinoamericano de Algebra, Biblioteca de la Revista Matematica Iberoamericana, Revista Matematica Iberoamericana, 2007, pp. 63-85 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155809 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14E15 | |
| dc.title | Rees algebras and resolution of singularities | |
| dc.type | text |