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arXiv · 1812.08531

Pathologies on the Hilbert scheme of points

Joachim Jelisiejew
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Abstract

We prove that the Hilbert scheme of points on a higher dimensional affine space is non-reduced and has components lying entirely in characteristic p for all primes p. In fact, we show that Vakil's Murphy's Law holds up to retraction for this scheme. Our main tool is a generalized version of the Bialynicki-Birula decomposition.

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Joachim Jelisiejew. 2019-11-28. Pathologies on the Hilbert scheme of points. https://arxiv.org/abs/1812.08531

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