Hilbert schemes and Betti numbers over Clements-Lindström rings

Satoshi Murai*, Irena Peeva

*この研究の対応する著者

研究成果: Article査読

3 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1337-1364
ページ数28
ジャーナルCompositio Mathematica
148
5
DOI
出版ステータスPublished - 2012 9
外部発表はい

ASJC Scopus subject areas

  • 代数と数論

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