Compactification of configuration spaces via Hilbert schemes
Algebraic Geometry
2007-05-23 v1
Abstract
Let F(X,n):= X^n-\Delta be the complementary of the union \Delta of the diagonals of X^n and let U be a quotient of F(X,n) (possibly trivial) by a subgroup of the symmetric group S_n. We construct compactifications of U in products of Hilbert schemes. Our approach generalizes and unifies classical constructions by Schubert-Semple, Le Barz-Keel, Kleiman and Cheah. An extensive study is done in the case n<4. This includes in particular a complete classification and a description of the quotients by the natural actions.
Cite
@article{arxiv.math/0107041,
title = {Compactification of configuration spaces via Hilbert schemes},
author = {Laurent Evain},
journal= {arXiv preprint arXiv:math/0107041},
year = {2007}
}
Comments
34 pages, in french