Generic initial ideals and squeezed spheres

研究成果: Article査読

11 被引用数 (Scopus)

抄録

In 1988 Kalai constructed a large class of simplicial spheres, called squeezed spheres, and in 1991 presented a conjecture about generic initial ideals of Stanley-Reisner ideals of squeezed spheres. In the present paper this conjecture will be proved. In order to prove Kalai's conjecture, based on the fact that every squeezed (d - 1)-sphere is the boundary of a certain d-ball, called a squeezed d-ball, generic initial ideals of Stanley-Reisner ideals of squeezed balls will be determined. In addition, generic initial ideals of exterior face ideals of squeezed balls are determined. On the other hand, we study the squeezing operation, which assigns to each Gorenstein* complex Γ having the weak Lefschetz property a squeezed sphere Sq (Γ), and show that this operation increases graded Betti numbers.

本文言語English
ページ(範囲)701-729
ページ数29
ジャーナルAdvances in Mathematics
214
2
DOI
出版ステータスPublished - 2007 10 1
外部発表はい

ASJC Scopus subject areas

  • Mathematics(all)

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