Hilbert schemes and Betti numbers over Clements-Lindström rings

Satoshi Murai*, Irena Peeva

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We show that the Hilbert scheme, that parameterizes all ideals with the same Hilbert function over a Clements-Lindström ring W, is connected. More precisely, we prove that every graded ideal is connected by a sequence of deformations to the lex-plus-powers ideal with the same Hilbert function. This is an analogue of Hartshorne's theorem that Grothendieck's Hilbert scheme is connected. We also prove a conjecture by Gasharov, Hibi, and Peeva that the lex ideal attains maximal Betti numbers among all graded ideals in W with a fixed Hilbert function.

Original languageEnglish
Pages (from-to)1337-1364
Number of pages28
JournalCompositio Mathematica
Issue number5
Publication statusPublished - 2012 Sept
Externally publishedYes


  • Betti numbers
  • Deformations
  • Hilbert scheme

ASJC Scopus subject areas

  • Algebra and Number Theory


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