Abstract
We consider graded artinian complete intersection algebras \(A=\mathbb {C}[x_0,\ldots ,x_m]/I\) with I generated by homogeneous forms of degree \(d\ge 2\). We show that the general multiplication by a linear form \(\mu _L:A_{d-1}\rightarrow A_d\) is injective. We prove that the Weak Lefschetz Property for holds for any c.i. algebra A as above with \(d=2\) and \(m\le 4\), previously known for \(m\le 3\).
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This work has been done within the framework of the national project “Geometry on Algebraic Varieties”, Prin (Cofin) 2015 of MIUR.
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Alzati, A., Re, R. Complete intersections of quadrics and the Weak Lefschetz Property. Collect. Math. 70, 283–294 (2019). https://doi.org/10.1007/s13348-018-0230-1
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DOI: https://doi.org/10.1007/s13348-018-0230-1