Mathematics – Algebraic Geometry
Scientific paper
2008-12-17
Mathematics
Algebraic Geometry
22 pages, 1 figure. Corrected typos. Included Macaulay2 code for computations cited in the paper at the end of the laTex versi
Scientific paper
We consider the question of which zero-dimensional schemes deform to a collection of distinct points; equivalently, we ask which Artinian k-algebras deform to a product of fields. We introduce a syzygetic invariant which sheds light on this question for zero-dimensional schemes of regularity two. This invariant imposes obstructions for smoothability in general, and it completely answers the question of smoothability for certain zero-dimensional schemes of low degree. The tools of this paper also lead to other results about Hilbert schemes of points, including a characterization of nonsmoothable zero-dimensional schemes of minimal degree in every embedding dimension d\geq 4.
Erman Daniel
Velasco Mauricio
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