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Mathematics > Algebraic Geometry

arXiv:1812.08531 (math)
[Submitted on 20 Dec 2018 (v1), last revised 28 Nov 2019 (this version, v2)]

Title:Pathologies on the Hilbert scheme of points

Authors: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.
Comments: 24 pages, some explicit examples, comments/questions welcome!
Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC)
MSC classes: 14C05, 14L30, 14B12, 13D10, 14B07
Report number: BCSim-2018-s09
Cite as: arXiv:1812.08531 [math.AG]
  (or arXiv:1812.08531v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.08531

Submission history

From: Joachim Jelisiejew [view email]
[v1] Thu, 20 Dec 2018 12:52:25 UTC (33 KB)
[v2] Thu, 28 Nov 2019 11:50:03 UTC (35 KB)
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