Complete intersections of quadrics and the Weak Lefschetz Property

• Autores: Alberto Alzati, Riccardo Re
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 70, Fasc. 2, 2019, págs. 283-294
• Idioma: inglés
• DOI: 10.1007/s13348-018-0230-1
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• Resumen

  • 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.

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