On Algorithmic Equiresolution and Stratification of Hilbert Schemes

Details On Algorithmic Equiresolution and Stratification of Hilbert Schemes On Algorithmic Equiresolution and Stratification of Hilbert Schemes

2000-10-25

arxiv.org/abs/math/0010228v1

Proc. London Math. Soc. (3) 86 (2003) 607-648

Mathematics

Algebraic Geometry

Plain TeX, 37 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On Algorithmic Equiresolution and Stratification of Hilbert Schemes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Algorithmic Equiresolution and Stratification of Hilbert Schemes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Algorithmic Equiresolution and Stratification of Hilbert Schemes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-105698