Lefschetz property and powers of linear forms in K[x, y, z]

Autor(es)

Almeida, Charles ^[1] ; Andrade, Aline V. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: FORUM MATHEMATICUM; v. 30, n. 4, p. 857-865, JUL 2018.
• Citações Web of Science: 0

Resumo

In {[}9], Migliore, Miro-Roig and Nagel proved that if R = K{[}x, y, z], where K is a field of characteristic zero, and I = (L-1(a1), ... , L-4(a4)) is an ideal generated by powers of four general linear forms, then the multiplication by the square L-2 of a general linear form L induces a homomorphism of maximal rank in any graded component of R/I. More recently, Migliore and Miro-Roig proved in {[}7] that the same is true for any number of general linear forms, as long the powers are uniform. In addition, they conjectured that the same holds for arbitrary powers. In this paper, we will prove that this conjecture is true, that is, we will show that if I = (L-1(a1),..., L-r(ar)) is an ideal of R generated by arbitrary powers of any set of general linear forms, then the multiplication by the square L-2 of a general linear form L induces a homomorphism of maximal rank in any graded component of R/I. (AU)

• Processo FAPESP: 16/14376-0 - Feixes reflexivos e sem torção em espaços projetivos
• Beneficiário: Charles Aparecido de Almeida
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado Direto
• Processo FAPESP: 14/08306-4 - Fibrados vetoriais sobre espaços projetivos
• Beneficiário: Charles Aparecido de Almeida
• Modalidade de apoio: Bolsas no Brasil - Doutorado Direto