It is known that graded cyclic modules over S = K[x,y] have the Weak Lefschetz Property (WLP). This is not true for non-cyclic modules over S. The purpose of this note is to study which conditions on S-modules ensure the WLP. We give an algorithm to test the WLP for graded modules with fixed Hilbert function. In particular, we prove that indecomposable graded modules over S with the Hilbert function (h0,h1) have the WLP.

On the weak Lefschetz property of graded modules over K[x, y]

FAVACCHIO, GIUSEPPE;
2012

Abstract

It is known that graded cyclic modules over S = K[x,y] have the Weak Lefschetz Property (WLP). This is not true for non-cyclic modules over S. The purpose of this note is to study which conditions on S-modules ensure the WLP. We give an algorithm to test the WLP for graded modules with fixed Hilbert function. In particular, we prove that indecomposable graded modules over S with the Hilbert function (h0,h1) have the WLP.
Lefschetz properties; Monomial ideals; Indecomposable module
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/243042
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