Compactification of configuration spaces via Hilbert schemes

Laurent Evain

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Compactification of configuration spaces via Hilbert schemes

Laurent Evain

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Abstract

Let F(X,n):= X^n-Δbe the complementary of the union Δof 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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BibTeX RIS

Laurent Evain. 2001-07-05. Compactification of configuration spaces via Hilbert schemes. https://arxiv.org/abs/math/0107041

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