Generic initial ideals and squeezed spheres

Details Generic initial ideals and squeezed spheres Generic initial ideals and squeezed spheres

2006-01-18

arxiv.org/abs/math/0601442v3

Mathematics

Commutative Algebra

28 pages, proofs in Section 5 and 6 are modified, an example of the squeezing operation is added, to appear in Adv. Math

Scientific paper

In 1988 Kalai construct a large class of simplicial spheres, called squeezed spheres, and in 1991 presented a conjectured 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 $\Gamma$ having the weak Lefschetz property a squeezed sphere $\mathrm{Sq}(\Gamma)$, and show that this operation increases graded Betti numbers.

Affiliated with

Also associated with

No associations

Rating

Generic initial ideals and squeezed spheres does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generic initial ideals and squeezed spheres, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generic initial ideals and squeezed spheres will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-594369