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

Giuseppe Favacchio; Phong Dinh Thieu

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

Commutative Algebra 2013-05-13 v1

Authors: Giuseppe Favacchio , Phong Dinh Thieu

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.

Keywords

weak Lefschetz property graded modules Hilbert function indecomposable modules polynomial rings commutative algebra

Cite

@article{arxiv.1305.2338,
  title  = {On the weak Lefschetz Property of graded modules over $K[x,y]$},
  author = {Giuseppe Favacchio and Phong Dinh Thieu},
  journal= {arXiv preprint arXiv:1305.2338},
  year   = {2013}
}

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