Hilbert schemes and Betti numbers over Clements-Lindström rings

Satoshi Murai, Irena Peeva

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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
Volume148
Issue number5
DOIs
Publication statusPublished - 2012 Sep 1
Externally publishedYes

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Hilbert Scheme
Betti numbers
Hilbert Function
Ring
Parameterise
Maximal Ideal
Analogue
Theorem

Keywords

  • Betti numbers
  • Deformations
  • Hilbert scheme

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Hilbert schemes and Betti numbers over Clements-Lindström rings. / Murai, Satoshi; Peeva, Irena.

In: Compositio Mathematica, Vol. 148, No. 5, 01.09.2012, p. 1337-1364.

Research output: Contribution to journalArticle

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