The space of generically étale families

Details The space of generically étale families The space of generically étale families

2007-03-12

arxiv.org/abs/math/0703329v2

Mathematics

Algebraic Geometry

28 pages; replaced $TS^{n-1} R\otimes R$ with $TS^{n-1,1} R$; simplified some proofs

Scientific paper

We construct a space $G^n_X$ and a rank $n$, generically etale family of closed subspaces in a separated ambient space $X$. The constructed pair satisfies a universal property of generically etale families of closed subspaces in $X$. This universal property is derived directly from the construction and does in particular not use the Hilbert scheme. The constructed space $G^n_X$ is by its universal property canonically identified with a closed subspace of the Hilbert scheme.

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