ON THE WEAK LEFSCHETZ PROPERTY FOR IDEALS GENERATED BY POWERS OF GENERAL LINEAR FORMS
Abstract
We provide a description of initial ideals for almost complete intersections generated by powers of general linear forms and prove that WLP in a fixed degree d holds when the number of variables n is sufficiently large compared to d. In particular, we show that if n≥3d−2 then WLP holds for the ideal generated by squares at the degree d spot and for n≥(3d−3)/2 WLP holds for ideal generated by cubes at the degree d spot. Finally, we prove that WLP fails for the ideal generated by squares when n
Fields of Study & Subjects
Commutative Algebra and Its Applications
Rings
Modules
and Algebras
Scheduling and Optimization Algorithms
Publication details
- Journal / source
- Journal of Commutative Algebra
- Volume
- 18
- Issue
- 2
- Pages
- 139–158
- Publication date
- 29 July 2026
- Language
- EN