Resumen de Complete intersections of quadrics and the Weak Lefschetz Property

Alberto Alzati, Riccardo Re

• We consider graded artinian complete intersection algebras ?=ℂ[?0,…,??]/? with I generated by homogeneous forms of degree ?≥2 . We show that the general multiplication by a linear form ??:??−1→?? is injective. We prove that the Weak Lefschetz Property for holds for any c.i. algebra A as above with ?=2 and ?≤4 , previously known for ?≤3 .