Smooth Hilbert schemes: their classification and geometry

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.

arXiv comment21 pages, v2 improves the exposition and corrects minor errors

References in corpus (1)

• The Ubiquity of Smooth Hilbert Schemes

Cited by in corpus (4)

• On the smoothness of lexicographic points on Hilbert schemes
• The geometry of Hilbert schemes of two points on projective space
• Some Singular Lex-Segments
• The sum of the Betti numbers of smooth Hilbert schemes