Monads on projective varieties

• Autor(a) principal: Marchesi, S.
• Data de Publicação: 2018
• Outros Autores: Marques, P. M., Soares, H.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10071/16230
• topic: Monads; ACM varieties

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.