Monads on projective 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...
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| Other Authors: | , |
| Format: | article |
| Language: | eng |
| Published: |
2018
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10071/16230 |
| Country: | Portugal |
| Oai: | oai:repositorio.iscte-iul.pt:10071/16230 |
| Summary: | 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. |
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