Compactification of configuration spaces via Hilbert schemes

Details Compactification of configuration spaces via Hilbert schemes Compactification of configuration spaces via Hilbert schemes

2001-07-05

arxiv.org/abs/math/0107041v1

Mathematics

Algebraic Geometry

34 pages, in french

Scientific paper

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.

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