Pathologies on the Hilbert scheme of points
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2018
- DOI:
- 10.48550/arXiv.1812.08531
- arXiv:
- arXiv:1812.08531
- Bibcode:
- 2018arXiv181208531J
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Commutative Algebra;
- 14C05;
- 14L30;
- 14B12;
- 13D10;
- 14B07
- E-Print:
- 24 pages, some explicit examples, comments/questions welcome!