Formal-local structure of the Hilbert scheme of points on three-dimensional complex affine space around special monomial ideals

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 disting...

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Bibliographic Details
Main Author: Hsu, Ting Chen Leo
Language:English
Published: University of British Columbia 2016
Online Access:http://hdl.handle.net/2429/57843
Description
Summary: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. === Science, Faculty of === Mathematics, Department of === Graduate