On the smoothness of lexicographic points on Hilbert schemes

Ramkumar, Ritvik; Sammartano, Alessio

doi:10.1016/j.jpaa.2021.106872

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2024

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“…A first example of a singular lex-segment ideal is given in [RS20]. Our examples broaden the class of known singular lex-segments and raise many interesting questions: Are all lexsegment points of this kind singular?…”

Section: Introductionmentioning

confidence: 92%

Some Singular Lex-Segments

Staal

2021

Preprint

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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 singular lex-segment points lying on two and three irreducible components. We find further singular lex-segment points at nearby Hilbert schemes. We conclude by showing that the analogous example at the Hilbert scheme of twisted cubics also has a singular lex-segment point.

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Section: Introductionmentioning

confidence: 92%