Syzygy Bundles on P^2 and the Weak Lefschetz Property

Details Syzygy Bundles on P^2 and the Weak Lefschetz Property Syzygy Bundles on P^2 and the Weak Lefschetz Property

2006-04-18

arxiv.org/abs/math/0604406v2

Mathematics

Algebraic Geometry

To appear in Illinois Journal of Mathematics

Scientific paper

Let K be an algebraically closed field of characteristic zero and let I=(f_1,...,f_n) be a homogeneous R_+-primary ideal in R:=K[X,Y,Z]. If the corresponding syzygy bundle Syz(f_1,...,f_n) on the projective plane is semistable, we show that the Artinian algebra R/I has the Weak Lefschetz property if and only if the syzygy bundle has a special generic splitting type. As a corollary we get the result of Harima et alt., that every Artinian complete intersection (n=3) has the Weak Lefschetz property. Furthermore, we show that an almost complete intersection (n=4) does not necessarily have the Weak Lefschetz property, answering negatively a question of Migliore and Miro-Roig. We prove that an almost complete intersection has the Weak Lefschetz property if the corresponding syzygy bundle is not semistable.

Affiliated with

Also associated with

No associations

Rating

Syzygy Bundles on P^2 and the Weak Lefschetz Property 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 Syzygy Bundles on P^2 and the Weak Lefschetz Property, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Syzygy Bundles on P^2 and the Weak Lefschetz Property will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-195706