We consider graded artinian complete intersection algebras A=C[x0,...,xm]/I with I generated by homogeneous forms of degree d2. We show that the general multiplication by a linear form L:Ad-1Ad is injective. We prove that the Weak Lefschetz Property for holds for any c.i. algebra A as above with d=2 and m4, previously known for m <= 3.
Complete intersections of quadrics and the weak Lefschetz property / A. Alzati, R. Re. - In: COLLECTANEA MATHEMATICA. - ISSN 0010-0757. - 70:2(2019), pp. 283-294. [10.1007/s13348-018-0230-1]
Complete intersections of quadrics and the weak Lefschetz property
A. Alzati;
2019
Abstract
We consider graded artinian complete intersection algebras A=C[x0,...,xm]/I with I generated by homogeneous forms of degree d2. We show that the general multiplication by a linear form L:Ad-1Ad is injective. We prove that the Weak Lefschetz Property for holds for any c.i. algebra A as above with d=2 and m4, previously known for m <= 3.
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