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math.AG2021
Small elementary components of Hilbert schemes of points
Matthew Satriano, Andrew P. Staal
We answer an open problem posed by Iarrobino in the '80s: is there an elementary component of the Hilbert scheme of points with dimension less than…
math.AG2021★ 1 cited
Hilbert Schemes with Two Borel-fixed Points in Arbitrary Characteristic
Andrew P. Staal
We extend the recent classification of Hilbert schemes with two Borel-fixed points to arbitrary characteristic. We accomplish this by synthesizing Reeves' algorithm for generating…
math.AG2021
Some Singular Lex-Segments
Andrew P. Staal
We study the component structures of some standard-graded Hilbert schemes closely related to a Hilbert scheme of curves studied by Gotzmann. In particular, we encounter examples of…