| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | FORUM MATHEMATICUM; v. 30, n. 4, p. 857-865, JUL 2018. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 16/14376-0 - Reflexive and torsion free sheaves on projective spaces |
| Grantee: | Charles Aparecido de Almeida |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate (Direct) |
| FAPESP's process: | 14/08306-4 - Vector bundles over projective spaces |
| Grantee: | Charles Aparecido de Almeida |
| Support Opportunities: | Scholarships in Brazil - Doctorate (Direct) |