The strong Lefschetz property of monomial complete intersections in two variables. (English) Zbl 1423.13083
A graded algebra \(A=\bigoplus_{i\geq 0} A_i\) is said to have the strong Lefschetz property if there is a linear form such that multiplication by any power of this linear form has maximal rank in every degree.
The present paper classifies the monomial complete intersections in two variables and of positive characteristic, which have the strong Lefschetz property.
This result, together with the previous works [R. P. Stanley, SIAM J. Algebraic Discrete Methods 1, 168–184 (1980; Zbl 0502.05004); M. Lindsey, Proc. Am. Math. Soc. 139, No. 1, 79–92 (2011; Zbl 1219.13001); D. Cook II, J. Algebra 369, 42–58 (2012; Zbl 1271.13010); S. Lundqvist and L. Nicklasson, J. Algebra 521, 213–234 (2019; Zbl 1409.13003)] gives a complete classification of the monomial complete intersections with the strong Lefschetz property.
The present paper classifies the monomial complete intersections in two variables and of positive characteristic, which have the strong Lefschetz property.
This result, together with the previous works [R. P. Stanley, SIAM J. Algebraic Discrete Methods 1, 168–184 (1980; Zbl 0502.05004); M. Lindsey, Proc. Am. Math. Soc. 139, No. 1, 79–92 (2011; Zbl 1219.13001); D. Cook II, J. Algebra 369, 42–58 (2012; Zbl 1271.13010); S. Lundqvist and L. Nicklasson, J. Algebra 521, 213–234 (2019; Zbl 1409.13003)] gives a complete classification of the monomial complete intersections with the strong Lefschetz property.
Reviewer: Eduardo Saenz-de-Cabezon (Logroño)
MSC:
| 13C40 | Linkage, complete intersections and determinantal ideals |
| 13F20 | Polynomial rings and ideals; rings of integer-valued polynomials |
References:
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