On Algorithmic Equiresolution and Stratification of Hilbert Schemes
| dc.creator | Encinas, S. | |
| dc.creator | Nobile, A. | |
| dc.creator | Villamayor, O. | |
| dc.date | 2000-10-25 | |
| dc.date.accessioned | 2026-07-07T04:38:13Z | |
| dc.date.available | 2026-07-07T04:38:13Z | |
| dc.description | Given an algorithm of resolution of singularities satisfying certain conditions (``good algorithms''), natural notions of simultaneous algorithmic resolution, or equiresolution, for families of embedded schemes (parametrized by a reduced scheme $T$) are proposed. It is proved that these conditions are equivalent. Something similar is done for families of sheaves of ideals, here the goal is algorithmic simultaneous principalization. A consequence is that given a family of embedded schemes over a reduced $T$, this parameter scheme can be naturally expressed as a disjoint union of locally closed sets $T_{j}$, such that the induced family on each part $T_{j}$ is equisolvable. In particular, this can be applied to the Hilbert scheme of a smooth projective variety; in fact, our result shows that, in characteristic zero, the underlying topological space of any Hilbert scheme parametrizing embedded schemes can be naturally stratified in equiresolvable families. | |
| dc.description | Plain TeX, 37 pages | |
| dc.identifier | https://arxiv.org/abs/math/0010228 | |
| dc.identifier | http://arxiv.org/abs/math/0010228 | |
| dc.identifier | Proc. London Math. Soc. (3) 86 (2003) 607-648 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60192 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14E15, 14D99 | |
| dc.title | On Algorithmic Equiresolution and Stratification of Hilbert Schemes | |
| dc.type | text |