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UBC Theses and Dissertations

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UBC Theses and Dissertations

Formal-local structure of the Hilbert scheme of points on three-dimensional complex affine space around special monomial ideals Hsu, Ting Chen Leo

Abstract

We show that the formal completion of the Hilbert scheme of points in ℂ³ at subschemes carved out by powers of the maximal ideal corresponding to the origin is given as the critical locus of a homogeneous cubic function. In particular, the Hilbert scheme is formal-locally a cone around these distinguished points.

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Attribution-NonCommercial-NoDerivatives 4.0 International