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FALL 2014 The strong Lefschetz property in codimension two
David Cook II
J. Commut. Algebra 6(3): 323-344 (FALL 2014). DOI: 10.1216/JCA-2014-6-3-323

Abstract

Every artinian quotient of $K[x,y]$ has the strong Lefschetz property if $K$ is a field of characteristic zero or is an infinite field whose characteristic is greater than the regularity of the quotient. We improve this bound in the case of monomial ideals. Using this we classify when both bounds are sharp. Moreover, we prove that the artinian quotient of a monomial ideal in $K[x,y]$ always has the strong Lefschetz property, regardless of the characteristic of the field, exactly when the ideal is lexsegment. As a consequence, we describe a family of non-monomial complete intersections that always have the strong Lefschetz property.

Citation

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David Cook II. "The strong Lefschetz property in codimension two." J. Commut. Algebra 6 (3) 323 - 344, FALL 2014. https://doi.org/10.1216/JCA-2014-6-3-323

Information

Published: FALL 2014
First available in Project Euclid: 17 November 2014

zbMATH: 1303.13019
MathSciNet: MR3278807
Digital Object Identifier: 10.1216/JCA-2014-6-3-323

Subjects:
Primary: 13A35 , 13E10

Keywords: lexsegment ideals , positive characteristic , strong Lefschetz property

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

Vol.6 • No. 3 • FALL 2014
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