Collectanea Mathematica

, Volume 70, Issue 2, pp 283–294 | Cite as

Complete intersections of quadrics and the Weak Lefschetz Property

  • Alberto Alzati
  • Riccardo ReEmail author


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 \(m\le 3\).


Weak Lefschetz Property Artinian algebra Complete intersection 

Mathematics Subject Classification

Primary 13A02 Secondary 14N05 


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Copyright information

© Universitat de Barcelona 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica F.EnriquesUniversità di MilanoMilanItaly
  2. 2.Dipartimento di Scienza e Alta TecnologiaUniversità dell’ InsubriaComoItaly

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