The Hilbert scheme of points on a threefold, I

The Hilbert scheme of points on a threefold, I

We investigate the Hilbert scheme of points on a smooth threefold. We introduce a notion of broken Gorenstein structure for finite schemes, and show that its existence guarantees smoothness on the Hilbert scheme. Moreover, we conjecture that it is exhaustive: every smooth point admits a broken Goren...

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Hauptverfasser: Jelisiejew, Joachim, Ramkumar, Ritvik, Sammartano, Alessio
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Mathematics - Algebraic Geometry
Mathematics - Commutative Algebra
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Ramkumar, Ritvik
Sammartano, Alessio
description We investigate the Hilbert scheme of points on a smooth threefold. We introduce a notion of broken Gorenstein structure for finite schemes, and show that its existence guarantees smoothness on the Hilbert scheme. Moreover, we conjecture that it is exhaustive: every smooth point admits a broken Gorenstein structure. We give an explicit characterization of the smooth points on the Hilbert scheme of A^3 corresponding to monomial ideals. We investigate the nature of the singular points, and prove several conjectures by Hu. Along the way, we obtain a number of additional results, related to linkage classes, nested Hilbert schemes, and a bundle on the Hilbert scheme of a surface.
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Mathematics - Commutative Algebra
title The Hilbert scheme of points on a threefold, I
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