Weak Lefschetz property of equigenerated complete intersections. Applications

2025/03/23 by Beorchia, Valentina, Miró-Roig, Rosa Maria
#13E10 #14F06 #14M10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.17991

Abstract

In this paper, we prove that any Artinian complete intersection homogeneous ideal I in K[x₀,⋯,x_n] generated by n+1 forms of degree d≥ 2 satisfies the weak Lefschetz property (WLP) in degree t< d+\lceil (d)/(n) \rceil. As a consequence, we get that the Jacobian ideal of a smooth 3-fold of degree d≥ 7 in \mathbb P⁴ satisfies the weak Lefschetz property in degree d, answering a recent question of Beauville.

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