TY - JOUR

T1 - Generic initial ideals and squeezed spheres

AU - Murai, Satoshi

N1 - Funding Information:
1 The author is supported by JSPS Research Fellowships for Young Scientists.

PY - 2007/10/1

Y1 - 2007/10/1

N2 - 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.

AB - 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.

KW - Algebraic shifting

KW - Generic initial ideals

KW - Graded Betti numbers

KW - Simplicial polytopes

KW - Simplicial spheres

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U2 - 10.1016/j.aim.2007.03.004

DO - 10.1016/j.aim.2007.03.004

M3 - Article

AN - SCOPUS:34447136304

VL - 214

SP - 701

EP - 729

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 2

ER -