Generic initial ideals and squeezed spheres

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11 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)701-729
Number of pages29
JournalAdvances in Mathematics
Volume214
Issue number2
DOIs
Publication statusPublished - 2007 Oct 1
Externally publishedYes

Keywords

  • Algebraic shifting
  • Generic initial ideals
  • Graded Betti numbers
  • Simplicial polytopes
  • Simplicial spheres

ASJC Scopus subject areas

  • Mathematics(all)

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