Pathologies on the Hilbert scheme of points

By Joachim Jelisiejew. Inventiones Mathematicae, 2018

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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 Białynicki-Birula decomposition.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/534417f9c0d8991dc39ed4a62dac133a0f3ee5bd