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arXiv · 1305.2338

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

Giuseppe Favacchio·Phong Dinh Thieu
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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 $(h_0,h_1)$ have the WLP.

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Giuseppe Favacchio, Phong Dinh Thieu. 2013-05-10. On the weak Lefschetz Property of graded modules over $K[x,y]$. https://arxiv.org/abs/1305.2338

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