| Texto completo | |
| Autor(es): |
Jorge-Perez, V. H.
;
Santos-Lima, J. A.
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | COMMUNICATIONS IN ALGEBRA; v. N/A, p. 20-pg., 2025-08-19. |
| Resumo | |
In this paper, we investigate the homological properties of the symmetric powers of finitely generated modules on a Noetherian local ring R, focusing on the computation of minimal free resolutions and Betti numbers associated with Sj(M), the j-th symmetric power of M. Motivated by results of Weyman, Tchernev, Avramov, and Molica-Restuccia on the acyclicity of the complexes SjF center dot, we study under what conditions the Betti numbers of Sj(M) can be determined from those of M. We prove that for modules M with a minimal finite free resolution satisfying the (SWj) condition, the complex SjF center dot yields a minimal free resolution of Sj(M) with finite projective dimension. We provide explicit formulas for the Betti numbers of Sj(M) in terms of those of M, including applications to linear-type modules and powers of ideals, as well as establishing upper and lower bounds for these invariants. As a consequence, we obtain special cases of the Buchsbaum-Eisenbud-Horrocks conjecture. (AU) | |
| Processo FAPESP: | 19/21181-0 - Novas fronteiras na Teoria de Singularidades |
| Beneficiário: | Regilene Delazari dos Santos Oliveira |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |