We consider graded artinian complete intersection algebras A= C[x, … , x m ] / I with I generated by homogeneous forms of degree d≥ 2. We show that the general multiplication by a linear form μ L : A d-1 → 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≤ 4 , previously known for m≤ 3.
Complete intersections of quadrics and the Weak Lefschetz Property
RE, RICCARDO
2019-01-01
Abstract
We consider graded artinian complete intersection algebras A= C[x, … , x m ] / I with I generated by homogeneous forms of degree d≥ 2. We show that the general multiplication by a linear form μ L : A d-1 → 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≤ 4 , previously known for m≤ 3.
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