Pathologies on the Hilbert scheme of points

@article{Jelisiejew2018PathologiesOT,
  title={Pathologies on the Hilbert scheme of points},
  author={Joachim Jelisiejew},
  journal={Inventiones mathematicae},
  year={2018},
  volume={220},
  pages={581-610}
}
  • Joachim Jelisiejew
  • Published 2018
  • Mathematics
  • Inventiones mathematicae
  • 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. 

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