MONADS ON PROJECTIVE VARIETIES

Autor(es)

Marchesi, Simone ^[1] ; Marques, Pedro Macias ^[2] ; Soares, Helena

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Cidade Univ Zeferino Vaz, Campinas, SP - Brazil

^[2] Univ Evora, Inst Invest & Formacao Avancada, Ctr Invest Matemat & Aplicacoes, Dept Matemat, Escola Ciencias & Tecnol, Evora - Portugal

• Tipo de documento: Artigo Científico
• Fonte: PACIFIC JOURNAL OF MATHEMATICS; v. 296, n. 1, p. 155-180, SEP 2018.
• Citações Web of Science: 0

Resumo

We generalize Floystad's theorem on the existence of monads on projective space to a larger set of projective varieties. We consider a variety X, a line bundle L on X, and a basepoint-free linear system of sections of L giving a morphism to projective space whose image is either arithmetically Cohen-Macaulay (ACM) or linearly normal and not contained in a quadric. We give necessary and sufficient conditions on integers a, b and c for a monad of type 0 -> (L-v)(a)-> O-X(b) -> L-c -> 0 to exist. We show that under certain conditions there exists a monad whose cohomology sheaf is simple. We furthermore characterize low-rank vector bundles that are the cohomology sheaf of some monad as above. Finally, we obtain an irreducible family of monads over projective space and make a description on how the same method could be used on an ACM smooth projective variety X. We establish the existence of a coarse moduli space of low-rank vector bundles over an odd-dimensional X and show that in one case this moduli space is irreducible. (AU)

• Processo FAPESP: 14/12558-9 - Mônadas em variedades projetivas, fibrados sizígia e álgebras de Artin Gorenstein
• Beneficiário: Marcos Benevenuto Jardim
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 14/00498-1 - Fibrados instanton generalizados em variedades projetivas suaves
• Beneficiário: Marcos Benevenuto Jardim
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 17/03487-9 - Fibrados vetoriais: da família instanton até uma nova regularidade
• Beneficiário: Simone Marchesi
• Modalidade de apoio: Auxílio à Pesquisa - Regular