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arXiv · 2008.08938

Smooth Hilbert schemes: their classification and geometry

Roy Skjelnes·Gregory G. Smith
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Abstract

Closed subschemes in projective space with a fixed Hilbert polynomial are parametrized by a Hilbert scheme. We classify the smooth ones. We identify numerical conditions on a polynomial that completely determine when the Hilbert scheme is smooth. We also reinterpret these smooth Hilbert schemes as generalized partial flag varieties and describe the subschemes being parametrized.

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Roy Skjelnes, Gregory G. Smith. 2020-08-20. Smooth Hilbert schemes: their classification and geometry. https://doi.org/10.1515/crelle-2022-0083

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